Answer:
Step-by-step explanation:
Hello!
Given the variable
X: reading speed of a second-grader. (words per minute)
From a random sample of second-grader the mean and standard deviation were:
X[bar]= 31.6 words per minute
S= 2.4 words per minute
To study the population mean (μ) you have the following sampling scenarios and need to choose the correct statistic.
Sampling scenarios:
(1) The sample has size 100, and it is from a non-normally distributed population with a known standard deviation of 2.6.
For this scenario you have to remember the Central Limit Theorem. The variable of study has a non-normal distribution but the sample is large enough (As a rule, a sample of size greater than or equal to 30 is considered sufficient to apply the theorem and use the approximation) you can approximate the distribution of the sample mean to normal: X[bar]≈N(μ;σ²/n); Then it is valid to use an approximation to the standard normal distribution to make inference statements about the population mean.
Statistic: Z
(2) The sample has size 75, and it is from a non-normally distributed population.
Same explanation as the statement before, except that the population variance is unknown. Since the distribution is already an approximation you can use its estimation (sample variance) for the statistic. (It would be less accurate than using the population variance but still valid)
Statistic: Z
(3) The sample has size 12, and it is from a population with a distribution about which we know very little.
To use a student's t the population needs to have a normal distribution, which is not the case, same goes for the standard normal.
To apply the central Limit Theorem you need a sample size equal or greater to 30, this is not the case.
For this sampling example neither distribution is applicable.
(4) The sample has size 14, and it is from a normally distributed population with a known standard deviation of 2.6.
The population has a normal distribution and the population standard deviation is known. The sample size is rather small but it isn't an impediment to apply the standard normal distribution. Also, even tough the population standard deviation is known, a student t is also applicable. In this case both statistics are a viable option.
Statistic: Z or t
(5) The sample has size 16, and it is from a normally distributed population with unknown standard deviation.
The population has a normal distribution, with unknown population standard deviation and the sample size is rather small. You can use a Student t to infer over the population mean.
Statistic: t
I hope this helps!
A notebook costs £1.30, a pen costs 38p , a pencil costs 21p and a sharpener costs 84p.
Remi buys 2 pencils, 3 pens, 2 sharpeners and some notebooks.
He pays with £10 and receives 26p change.
How many notebooks did he buy?
Answer:5
Step-by-step explanation:
Tennis elbow is thought to be aggravated by the impact experienced when hitting the ball. The article "Forces on the Hand in the Tennis One-Handed Backhand" (Int. J. of Sport Biomechanics (1991) reported the force (N) on the hand just after impact on a one- handed backhand drive for six advanced players and for eight intermediate players.
Advanced 44.70 26.31 55.75 28.54 46.99 39.46
Intermediate 15.58 19.16 24.13 10.56 32.88 21.47 14.32 33.09
1. Do the data shown above indicate that the mean force after impact is greater for advanced tennis players than it is for intermediate players?
2. Do a hypothesis test at .05 confidence level.
Answer:
Step-by-step explanation:
Hello!
The objective is to study whether there is a greater force after impacting on one- handed backhand drive in advanced tennis players than in intermediate tennis players.
Sample 1: Advanced tennis players
X₁: Force (N) on the hand just after impact on a one- handed backhand drive for an advanced tennis player.
n₁= 6
X[bar]₁= 40.29 N
S₁= 11.29
Sample 2: Intermediate players
X₂: Force (N) on the hand just after impact on a one- handed backhand drive for an intermediate tennis player.
n₂= 8
X[bar]₂= 21.40
S₂= 8.30
Assuming that both variables have a normal distribution and both population variances are equal, to compare these two populations is best to do so trough their population means using a t-test for independent samples.
If the force is greater for the advanced players than for the intermediate players, then you'd expect the population mean for the advanced players to be greater than the population mean for the intermediate players:
H₀: μ₁ ≤ μ₂
H₁: μ₁ > μ₂
α: 0.05
[tex]t= \frac{(X_[bar]_1-X[bar]_2)-(Mu_1-Mu_2)}{Sa\sqrt{\frac{1}{n_1} +\frac{1}{n_2} } } ~~t_{n_1+n_2-2}[/tex]
[tex]Sa= \sqrt{\frac{(n_1-1)S_1^2+(n_2-1)S_2^2}{n_1+n_2-2} } = \sqrt{\frac{5*127.51+7*68.92}{6+8-2} }= 9.66[/tex]
[tex]t_{H_0}= \frac{(40.29-21.40)-0}{9.66\sqrt{\frac{1}{6} +\frac{1}{8} } } = 3.62[/tex]
Using the p-value approach, the decision rule is
If p-value ≤ α, reject the null hypothesis
If p-value > α, do not reject the null hypothesis
The p-value for this test is 0.00024, it is less than the level of significance, so the decision is to reject the null hypothesis.
This means that at a 5% significance level you can conclude that the average force experienced on the hand after a one-handed backhand drive for advanced players is greater than the average force experienced on the hand after a one-handed backhand drive for intermediate players.
I hope this helps!
The National Center for Educational Statistics surveyed 5400 college graduates about the lengths of time required to earn their bachelors degrees. The mean is 5.4 years and the standard deviation is 1.9 years. Based on this sample, construct a 90% confidence interval for the mean time required by all college graduates
Answer:
The 90% confidence interval for the mean time required by all college graduates is between 5.36 years and 5.44 years.
Step-by-step explanation:
We have that to find our [tex]\alpha[/tex] level, that is the subtraction of 1 by the confidence interval divided by 2. So:
[tex]\alpha = \frac{1-0.9}{2} = 0.05[/tex]
Now, we have to find z in the Ztable as such z has a pvalue of [tex]1-\alpha[/tex].
So it is z with a pvalue of [tex]1-0.05 = 0.95[/tex], so [tex]z = 1.645[/tex]
Now, find the margin of error M as such
[tex]M = z*\frac{\sigma}{\sqrt{n}}[/tex]
In which [tex]\sigma[/tex] is the standard deviation of the population and n is the size of the sample.
[tex]M = 1.645*\frac{1.9}{\sqrt{4500}} = 0.04[/tex]
The lower end of the interval is the sample mean subtracted by M. So it is 5.4 - 0.04 = 5.36 years.
The upper end of the interval is the sample mean added to M. So it is 5.4 + 0.04 = 5.44 years.
The 90% confidence interval for the mean time required by all college graduates is between 5.36 years and 5.44 years.
find the complete factored form of the polynomial 48m^5+8n^2
Answer:
8 ( 6 m 5^ + n 2^ )
Answer:
8( 6m^5 + n^2)
Step-by-step explanation:
48m^5+8n^2
Factor out 8
8* 6m^5 + 8 * n^2
8( 6m^5 + n^2)
Ajar contains 12 red balls, 7 green balls, 10 white balls, and 7 yellow balls.
Two balls are chosen from the jar, with replacement. What is the
probability that both balls chosen are green? Is this a dependent or
independent event? *
A. Independent, 1/30
B. Dependent, 1/30
C. Independent, 49/1296
D. Dependent, 49/1296
Answer:
C. Independent, 49/1296
Step-by-step explanation:
A jar contains 12 red balls, 7 green balls, 10 white balls, and 7 yellow balls.
Total balls = 12+7+10+7
Total balls= 36
Two balls are chosen at random with replacement.
The probability that the both balls are green = probability of the first ball to he green * probability of the second ball to be green
The probability that the both balls are green= 7/36 * 7/36
The probability that the both balls are green= 49/1296
The probability that the both balls are green= 49/1296
Please help I will mark you a brainliest
Answer:
[tex]sin\;60 =\frac{\sqrt{3} }{2}[/tex]
Which sequence of transformations on the red triangle will map it onto the missing portion of the square?
Answer:
A 90° counterclockwise rotation about the origin and then a translation 16 units right and 16 units up
Solution -Rotating the triangle 90° counterclockwise will take the triangle to 3rd quadrant and then further moving it 16 steps right will take it to 4th quadrant and followed by 16 steps upward will take it to the desired position which is in 1st quadrant.
Luke invested $69,000 in an account paying an interest rate of 5.1% compounded daily. Assuming no deposits or withdrawals are made, how much money, to the nearest dollar, would be in the account after 19 years?
Answer:
A = $ 181,824 rounded
Step-by-step explanation:
A = $ 181,823.93
A = P + I where
P (principal) = $ 69,000.00
I (interest) = $ 112,823.93
A professor notices that more and more students are using their notebook computers in class, presumably to take notes. He wonders if this may actually improve academic success. To test this, the professor records the number of times each student uses his or her computer during a class for one semester and the final grade in the class (out of 100 points). If notebook computer use during class is related to improved academic success, then a positive correlation should be evident. Given the following data, test whether notebook computer use and grades are related at a .05 level of significance.
State the conclusions for this test using APA format. First, describe the correlation coefficient in words and give the value of r. Then give the value of R2 and describe (in words) the effect size using the coefficient of determination. Finally, is there a significant relationship?
Answer:
Step-by-step explanation:
The hypothesis being tested is:
H0: ρ = 0
Ha: ρ ≠ 0
Pearson's r is -0.140.
The critical r-value is 0.404.
Since 0.140 < 0.404, we cannot reject the null hypothesis.
Therefore, we cannot conclude that notebook computer use and grades are related.
Pearson's r is -0.140. It means that there is a weak negative relationship between notebook computer use and grades.
The coefficient of determination is 0.020. 2% of the variation in the model is explained.
The relationship is not significant.
Notebook Computer Use Final Grade for Course
30 86
23 88
6 94
0 56
24 78
36 72
10 80
0 90
0 82
8 60
12 84
18 74
0 78
32 66
36 54
12 98
8 81
18 74
22 70
38 90
5 85
29 93
26 67
10 80
r² = 0.020
r = -0.140
Std. Error = 11.996
n = 24
k = 1
ANOVA table
Source SS df MS F p-value
Regression 63.6652 1 63.6652 0.44 0.5129
Residual 3,165.668 22 143.8940
Total 3,229.333 23
Solve the system by elimination: 4x+7y=-1 8x-4z=36 6y-4z=-22
An analogy: For this set of questions, choose between two cars that we will call "A" and "B." Car A is a two-door coupe. It gets 60 miles per gallon and has a 10-gallon tank. Car B is an SUV. It gets 2 miles per gallon and has a 60-gallon tank. Suppose both cars embark on a very long journey together, side by side, each with a full tank of gas. Which car holds more fuel?
Car B, the SUV, obviously holds more fuel after 0 driven miles, 60 gallons, while car A holds 10 gallons after 0 miles.
let's speak about miles with the abbreviation x.
sk at x=0 Car B got more fuel.
Car A gets 60 Miles per gallon, it's consuming 1/60 gallon per mile. The amount of fuel decreases by 1/60 per mile
After each mile, or each x-step, Car A has
This can be expressed mathematically:
A(x) = -1/60*x + 10
The -1/60x is, again, the consumption per mile, the +10 is the full tank at the start.
A(0)= -1/60*0 + 10
=10
For Car B the consumption is 1/2 gallons per mile and the tank holds 60 gallons of fuel, wich ammount is decreases with traveled distance.
B(x) = -1/2*x + 60
See that we could draw these two functions as lines in a coordinate system. (I did it with desmos btw). This step is just to help understand.
After some distance/ amount x of miles, Car A will hold more fuel than car B, because it drives more efficiently.
In the picture we can see that this is after about 100 miles and we could guess the amount of fuel, but I won't. Let's calculate it and then answer the question precisely.
We get the intersection of the two lines by setting them equal, a(x)=b(x)
-1/60x + 10 = -1/2x + 60
Exactly one point lies, equally, on both lines
So let's solve for x
Further on the right, each step is explained. we have to do the same operation on both sides of the equation, just to not break it.
-1/60x + 10 = -1/2x + 60 | -10
-1/60x = -1/2x + 50 | + 1/2x
-1/60x + 1/2x = 50 | *60
-1x + 30x = 3000
29x = 3000 | /29
x = 103.448275862
so after about 103.45 miles, Car B holds less fuel than Car A (and Car A more than Car B), until both are empty. Car B could therefore drive more miles
We can also ask how much fuel is left in both tanks at the intersection point by plugging the x-value we got into one of the equations (doesn't matter which one, since the point is the same)
a(103.4482) = -1/60 * 103.4482 + 10 = 8.28
If you want it to be precise, stay with fractions
a(3000/29) = -1/60 * 3000/29 + 10
= -50/29 +10
= 9 -21/29
= 8 + 8/29
Finding out how far each car could travel would be achieved by setting their fuel-equation equal to 0, because that's the value of it when they run of of fuel. For example 0 = -1/60x+10, then you (just) solve for x.
I did overshoot the given problem to offer offer you understanding that's spans more of the topic you are dealing with
(would really appreciate the brainliest)
[Pic] Find the volume of the pyramid.
Answer:
Step-by-step explanation:
Academic Advising: In 2014, the Community College Survey of Student Engagement reported that 32% of the students surveyed rarely or never use academic advising services. Since then, a local California community college that participated in the survey hired several new academic counselors and focused on outreach efforts to increase student awareness of available services. The counseling office staff then conducted a survey of 500 randomly selected students at the college, and 26% of those students said that they rarely or never use academic advising services. Campus administrators want to know whether the hiring and outreach efforts increased student use of academic advising. Which alternative hypothesis is appropriate?
Answer:
The alternative hypothesis is that the proportion of the students surveyed that rarely or never use academic advising services is less than 32% or 0.32. That is the students use of academic advising has increased.
Ha: p < 0.32
Step-by-step explanation:
The null hypothesis (H0) tries to show that no significant variation exists between variables or that a single variable is no different than its mean. While an alternative Hypothesis (Ha) attempt to prove that a new theory is true rather than the old one. That a variable is significantly different from the mean.
For the case above;
Let p represent the proportion of the students surveyed that rarely or never use academic advising services.
The null hypothesis is that the proportion of the students surveyed that rarely or never use academic advising services is equal to 32% or 0.32.
H0: p = 0.32
The alternative hypothesis is that the proportion of the students surveyed that rarely or never use academic advising services is less than 32% or 0.32. That is the students use of academic advising has increased.
Ha: p < 0.32
which best describes the triangle?
a) isosceles
b) acute
c) scalene
d) equilateral
Answer:
[tex]scalene \: triangle[/tex]
Step-by-step explanation:
The above given triangle represents the unequal lengths of three sides properties of scalene triangle
hence, it's a scalene triangle♥Hope this helps you out!!!
A = 4 0 0 1 3 0 −2 3 −1 Find the characteristic polynomial for the matrix A. (Write your answer in terms of λ.) Find the real eigenvalues for the matrix A. (Enter your answers as a comma-separated list.) λ = Find a basis for each eigenspace for the matrix A.
Answer:
Step-by-step explanation:
We are given the matrix
[tex] A = \left[\begin{matrix}4&0&0 \\ 1&3&0 \\-2&3&-1 \end{matrix}\right] [/tex]
a) To find the characteristic polynomial we calculate [tex]\text{det}(A-\lambda I)=0[/tex] where I is the identity matrix of appropiate size. in this case the characteristic polynomial is
[tex]\left|\begin{matrix}4-\lambda&0&0 \\ 1&3-\lambda&0 \\-2&3&-1-\lambda \end{matrix}\right|=0[/tex]
Since this matrix is upper triangular, its determinant is the multiplication of the diagonal entries, that is
[tex](4-\lambda)(3-\lambda)(-1-\lambda)=(\lambda-4)(\lambda-3)(\lambda+1)=0[/tex]
which is the characteristic polynomial of A.
b) To find the eigenvalues of A, we find the roots of the characteristic polynomials. In this case they are [tex]\lambda=4,3,-1[/tex]
c) To find the base associated to the eigenvalue lambda, we replace the value of lambda in the expression [tex]A-\lambda I[/tex] and solve the system [tex](A-\lambda I)x =0[/tex] by finding a base for its solution space. We will show this process for one value of lambda and give the solution for the other cases.
Consider [tex]\lambda = 4[/tex]. We get the matrix
[tex]\left[\begin{matrix}0&0&0 \\ 1&-1&0 \\-2&3&-5 \end{matrix}\right] [/tex]
The second line gives us the equation x-y =0. Which implies that x=y. The third line gives us the equation -2x+3y-5z=0. Since x=y, it becomes y-5z =0. This implies that y = 5z. So, combining this equations, the solution of the homogeneus system is given by
[tex](x,y,z) = (5z,5z,z) = z(5,5,1)[/tex]
So, the base for this eigenspace is the vector (5,5,1).
If [tex]\lambda = 3[/tex] then the base is (0,4,3) and if [tex]\lambda = -1[/tex] then the base is (0,0,1)
Carrie rolls 2 fair dice and adds the results from each. Work out the probability of getting a total of 9
Answer:
Probability of a sum of 9 = 0.111111
OR
Probability of a sum of 9 = 1/9
Step-by-step explanation:
Carrie rolls 2 fair dice and adds the results from each.
The total sample space = 36
Gotten from 6²= 36
The probability of getting a total of 9
Now let's look at the possible sum to give us a 9 (3 and 6, 4 and 5) twice.
So we gave number of occurrence of 9 to be four.
Probability of a sum of 9 = 4/36
Probability of a sum of 9 =1/9
Probability of a sum of 9 = 0.111111
The probability of getting a total of 9 is 0.111111 and this can be determined by using the concept of probability.
Given :
Carrie rolls 2 fair dice and adds the results from each.
The sample space is equal to [tex]6^2[/tex] that is 36. The numbers require on both the dices to get the sum equal to 9 are 4 and 5 or 6 and 3.
So, there is a total of 4 numbers in 36 sample size in order to get the sum of 9.
Now, the probability of getting a total of 9 is given by:
[tex]\rm P=\dfrac{4}{36}[/tex]
Further, simplify the above expression.
[tex]\rm P = \dfrac{1}{9}[/tex]
P = 0.111111
So, the probability of getting a total of 9 is 0.111111.
For more information, refer to the link given below:
https://brainly.com/question/23017717
Please answer this correctly
Answer:
5 cm
Step-by-step explanation:
Use lenght times wight times height
So, you need to do 4 times 4 times ________ is 80
find the y intercept!
Answer:
-23
Step-by-step explanation:
We note that as x increases by 36 from -72 to 36, y decreases by 24 from 25 to 1.
Increasing x from -36 by another 36 to zero will correspond to a decrease in y by another 24 from 1 to -23.
The y-intercept is -23.
_____
You could go to the trouble to use these observations to compute the slope as -24/36 = -2/3. Then you could pick one of the points and write the equation in point-slope form as ...
y = -2/3(x +36) +1 . . . point-slope form with m=-2/3, (h, k) = (-36, 1)
y = -2/3x -24 +1 . . . . . eliminate parentheses
y = -2/3x -23 . . . . . . . y-intercept is -23
Suppose an actual census showed that 20% of the households in Michigan have incomes in excess of $60,000. Assume that a random sample of 500 households in Michigan is taken. Then, the standard error of the sampling distribution of sample proportion of households who have incomes in excess of $60,000 will be:
Answer: 0.0179
Step-by-step explanation:
We know that , the standard error of the sampling distribution of sample proportion (p) is given by :-
[tex]S.E.=\sqrt{\dfrac{p(1-p)}{n}}[/tex]
where , n= sample size
Let p be the proportion of households who have incomes in excess of $60,000 .
As per given , we have
p= 20% = 0.20
n= 500
Then,
[tex]S.E.=\sqrt{\dfrac{0.20(1-0.20)}{500}}=\sqrt{\dfrac{0.20\times0.80}{500}}\\\\=\sqrt{0.00032}\\\\=0.01788854382\approx0.0179[/tex]
Hence, the standard error of the sampling distribution of sample proportion of households who have incomes in excess of $60,000 is 0.0179.
The standard error of the sampling distribution of sample proportion of households who have incomes in excess of $60,000 will be 0.0179.
Calculation of the standard error:Since an actual census showed that 20% of the households in Michigan have incomes in excess of $60,000.
So here the standard error should be
[tex]\sqrt (.2\times (1-.2)\div 500) \\\\= 0.0179[/tex]
Hence, the standard error should be 0.0179.
Learn more about sample here: https://brainly.com/question/9222927
6 times a number plus 22 is greater than 7
Answer: A
Step-by-step explanation: A is the correct answer because once you do the math (6*5/2+22) it gives you the correct amount. You also need to pay attention to the greater then and less than signs so that you don’t get confused.
If you found this answer helpful, give it a five star rating and a thanks!
(Even a brainliest if you want ;D)
Answer:a
Step-by-step explanation:
A clown has a silly string that is a 52cm long and magic scarf that is 28cm long.
How long are the clown's silly string and magic scarf combined?
Answer:
you asked about Telugu movies I see Telugu moviesI am from India telangana
What general conclusions can be drawn when you compare salaries with education levels?
Answer:
typically, careers that require higher education levels pay higher salaries than those that require a high school diploma.
A box has a volume of 22 1/2 in³. Find the length of the box!
Answer:
Length = 2.823 in (to 3 decimal places)
Step-by-step explanation:
assuming that the box is a cubic box:
volume of box = [tex]22\frac{1}{2}[/tex] in³ = 22.5 in³
volume = Length × Length × Length = (Length)³
∴ (Length)³ = 22.5
∴ Length = ∛(22.5)
using the calculator punch ∛(22.5), and the answer is:
∴ Length = 2.823 in (to 3 decimal places)
HELP PLEASE!!!
For what value of x does 4^x= (1/8)^x+5
answers:
-15 - 3 3 15
HELP PLEASE!!!
Answer:
Create equivalent expressions in the equation that all have equal bases, then solve for
x
.
Exact Form:
5/3
Decimal Form:
x
=
1.6
Mixed Number Form:
x
=
1 2/3
Answer:-3
Step-by-step explanation:
Please help me out:/
Answer:
Step-by-step explanation:
Select the correct answer.
What is 22% of 50?
OA.
44
OB.
28
Oc.
22
OD.
11
Answer:
11
Step-by-step explanation:
A random sample of 100 college students is taken from the student body of a large university Assume that, in fact, a population mean of 20 hours and a standard deviation of 15 hours describe the weekly study estimates for the entire student body. Therefore, the sampling distribution of the mean has a mean that:________.
a) approximates 20 hours.
b) equals 20 hours.
c) lies within a couple of hours of 20.
d) equals the one observed sample mean.
Answer:
b) equals 20 hours.
Step-by-step explanation:
The sampling distribution of means refers to the distribution of all the possible sample means, with a certain sample size (in this case, n=100) extracted from the population.
The sampling distribution of the means is equal to the population mean. That does not mean that every sample will result in a mean equal to the population, but that the population of sample means will have an average of 20 hours.
A group of scientists wants to investigate if they can predict the life expectancy
Step-by-step explanation:
There is no question asked here, bit of course it is possible to predict the life expectancies of a lot of things. This takes patience, resistance, and persistence, because working on something that takes time without persistence would result in a painful waste of time.
To predict the life expectancy of an effect is to predict how long it is going to take before it goes extinct, or seize from existence.
At a time denoted as t=0, a student carrying a new flu virus comes back to an isolated campus that has a fixed number of 1000 people. Determine a differential equation for the number of people x(t) who have contracted the flu if the rate at which the disease spreads is proportional to the number of interactions between the people who have the flu and the number of people who have not yet been exposed to it. (Please use k as the proportional constant.)
Answer:
[tex]\dfrac{dx(t)}{dt} = kx(t)[1000-x(t)],$ x(0)=0[/tex]
Step-by-step explanation:
Total Number of People on Campus =1000
Let the number of people who have contracted the flu =x(t)
Therefore, the number of people who have not contracted the flu =1000-x(t)
Since the rate at which the disease spreads is proportional to the number of interactions between the people who have the flu and the number of people who have not yet been exposed to it.
[tex]\dfrac{dx(t)}{dt} \propto x(t)[1000-x(t)][/tex]
Introducing the proportional constant k, we obtain:
[tex]\dfrac{dx(t)}{dt} = kx(t)[1000-x(t)][/tex]
At t=0, there was no infected on the campus, therefore the initial condition is given:
[tex]x(0)=0[/tex]
Therefore, a differential equation for the number of people x(t) who have contracted the flu is:
[tex]\dfrac{dx(t)}{dt} = kx(t)[1000-x(t)],$ x(0)=0[/tex]
Find the indicated probability. The weekly salaries of teachers in one state are normally distributed with a mean of $490 and a standard deviation of $45. What is the probability that a randomly selected teacher earns more than $525 a week
Given Information:
Mean weekly salary = μ = $490
Standard deviation of weekly salary = σ = $45
Required Information:
P(X > $525) = ?
Answer:
P(X > $525) = 21.77%
Step-by-step explanation:
We want to find out the probability that a randomly selected teacher earns more than $525 a week.
[tex]P(X > 525) = 1 - P(X < 525)\\\\P(X > 525) = 1 - P(Z < \frac{x - \mu}{\sigma} )\\\\P(X > 525) = 1 - P(Z < \frac{525 - 490}{45} )\\\\P(X > 525) = 1 - P(Z < \frac{35}{45} )\\\\P(X > 525) = 1 - P(Z < 0.78)\\\\[/tex]
The z-score corresponding to 0.78 from the z-table is 0.7823
[tex]P(X > 525) = 1 - 0.7823\\\\P(X > 525) = 0.2177\\\\P(X > 525) = 21.77 \%[/tex]
Therefore, there is 21.77% probability that a randomly selected teacher earns more than $525 a week.
How to use z-table?
Step 1:
In the z-table, find the two-digit number on the left side corresponding to your z-score. (e.g 0.7, 2.2, 1.5 etc.)
Step 2:
Then look up at the top of z-table to find the remaining decimal point in the range of 0.00 to 0.09. (e.g. if you are looking for 0.78 then go for 0.08 column)
Step 3:
Finally, find the corresponding probability from the z-table at the intersection of step 1 and step 2.