Complete Question
Problem 9-8 (modified). The height of adult males in a particular city is normally distributed, with mean 69.5 in. and standard deviation 2.65 in.
When a random sample is taken of size 20, find (1) the standard error of Xbar
(2) the probability that Xbar falls within .5 in. of the true mean
Probability=
Answer:
1
[tex]\sigma_{\= x} = 0.5926[/tex]
2
[tex]P( 69 < \= X < 70) = 0.60134[/tex]
Step-by-step explanation:
From the question we are told that
The true mean is [tex]\mu = 69.5 \ in[/tex]
The standard deviation is [tex]\sigma = 2.65 \ in[/tex]
The sample size is n = 20
Generally the standard error of Xbar[tex](\= x)[/tex] is mathematically represented as
[tex]\sigma_{\= x} = \frac{\sigma }{\sqrt{n} }[/tex]
=> [tex]\sigma_{\= x} = \frac{ 2.65 }{\sqrt{ 20 } }[/tex]
=> [tex]\sigma_{\= x} = 0.5926[/tex]
Generally for [tex]\= x[/tex] to fall within 0.5 of the true mean the [tex]\= x[/tex] must be within
[tex]a = \mu + 0.5[/tex]
=> [tex]a = 69.5 + 0.5[/tex]
=> [tex]a = 70[/tex]
or [tex]b = \mu -0.5[/tex]
=> [tex]b = 69.5 -0.5[/tex]
=> [tex]b = 69[/tex]
Generally the probability that [tex]\= x[/tex] fall with 0.5 of the true mean is mathematically represented as
[tex]P( 69 < \= X < 70) = P(\frac{69 - 69.5 }{ 0.5926} < \frac{\= X - \mu }{ \sigma_{\= x} } <\frac{70- 69.5 }{ 0.5926})[/tex]
=> [tex]P( 69 < \= X < 70) = P(-0.844 < Z < 0.844)[/tex]
=> [tex]P( 69 < \= X < 70) = P( Z < 0.844) - P( < -0.844)[/tex]
From the z table the probability of ( Z < 0.844) and ( Z < -0.844) is
[tex]P( Z < 0.844) = 0.80067[/tex]
and
[tex]P( Z < - 0.844) = 0.19933[/tex]
So
[tex]P( 69 < \= X < 70) = 0.80067 - 0.19933[/tex]
=> [tex]P( 69 < \= X < 70) = 0.60134[/tex]
The standard error of the given data comes to be 0.593.
It is given that
mean [tex]\mu[/tex] = 69.5 inch
Standard deviation [tex]\sigma[/tex] = 2.65 inch
Sample size n =20
What is the standard error?The standard error is a statistical term that measures the accuracy with which a sample distribution represents a population by using standard deviation.
The standard error is given by:
[tex]SE =\frac{\sigma}{\sqrt{n} }[/tex]
[tex]SE =\frac{2.65}{\sqrt{20} }[/tex]
[tex]SE=0.593[/tex]
Hence, the standard error of the given data comes to be 0.593.
To get more about standard errors visit:
https://brainly.com/question/1191244
What is 9.023 as a mixed number
what is 1/4 mutipled by 2 1/2
Answer:
5/8
Step-by-step explanation:
Simplify the following:
(2 + 1/2)/4
Put 2 + 1/2 over the common denominator 2. 2 + 1/2 = (2×2)/2 + 1/2:
((2×2)/2 + 1/2)/4
2×2 = 4:
(4/2 + 1/2)/4
4/2 + 1/2 = (4 + 1)/2:
((4 + 1)/2)/4
4 + 1 = 5:
(5/2)/4
5/2×1/4 = 5/(2×4):
5/(2×4)
2×4 = 8:
Answer: 5/8
Fourteen more than three times a number is sixty-seven.
Answer:
67 = 3n + 14
Step-by-step explanation:
So we know its going to equal 67, and 3 times a number is the same as 3n more than is to show addition. That means you are adding 14 to 3n.
That's why it would be,
14 + 3n = 67
Hope that helps and have a great day!
Answer:
8[tex]\frac{1}{3}[/tex]
Step-by-step explanation:
67 ÷ 3 - 14
22[tex]\frac{1}{3}[/tex] - 14
8[tex]\frac{1}{3}[/tex]
Hope this helps!
Have a nice day!
If you find my answer helpful
Pls consider marking my answer as Brainliest! It would mean a lot!
Suppose the weather at Chebyshev Citadel is either sunny or cloudy. A sunny day is followed by a sunny day with probability 0.7, and a cloudy day is followed by a sunny day with probability 0.5. If it is sunny today, what is the probability that it will be sunny 3 days later
Answer:
0.628
Step-by-step explanation:
From the information given:
Let S represent sunny days and C represent cloudy days;
S is expressed in the matrix to be in the first row and first column
C is expressed in the matrix to be in the second row and second column
Then, the transition for the probability matrix can be computed as follows:
[tex]P = \right. \left[\begin{array}{cc}0.7&0.3\\0.5&0.5\\\end{array}\right][/tex]
[tex]P^2 = \right. \left[\begin{array}{cc}0.7&0.3\\0.5&0.5\\\end{array}\right] \right. \left[\begin{array}{cc}0.7&0.3\\0.5&0.5\\\end{array}\right][/tex]
[tex]P^2 = \right. \left[\begin{array}{cc}0.49+0.15&0.21+0.15\\0.35+0.25&0.15+0.25\\\end{array}\right] \right.[/tex]
[tex]P^2 = \right. \left[\begin{array}{cc}0.64&0.36\\0.60&0.40\\\end{array}\right] \right.[/tex]
[tex]P^3 = \right. \left[\begin{array}{cc}0.64&0.36\\0.60&0.40\\\end{array}\right] \right. \right. \left[\begin{array}{cc}0.7&0.3\\0.5&0.5\\\end{array}\right][/tex]
[tex]P^3 = \right. \left[\begin{array}{cc}0.628&0.372\\0.62&0.38\\\end{array}\right] \right.[/tex]
So, if it is sunny, the probability that it is going to be sunny 3 days later = 0.628
Using the transition of the events, it is found that there is a 0.628 = 62.8% probability that it will be sunny 3 days later.
The transition of events, considering that it is sunny today and we want it to be sunny 3 days later, is given by:
S - S - S - S
S - C - S - S
S - S - C - S
S - C - C - S
Considering the probabilities stated in the exercise(S - S: 0.7, S - C: 0.3, C - S: 0.5, C - C: 0.5), for the last three days, the probability is:
[tex]p = 0.7^3 + 0.3(0.5)(0.7) + 0.7(0.3)(0.5) + 0.3(0.5)(0.5) = 0.628[/tex]
0.628 = 62.8% probability that it will be sunny 3 days later.
A similar problem is given at https://brainly.com/question/22410644
What is the standard form of the equation of the circle in the graph
Answer:
the dot is the 0 rember dat
Step-by-step explanation:
Answer:it’s c
Step-by-step explanation:
the questions is c
Darin in recorded the height of a tree planted from a seed at different time intervals.His data is shown in the table below
Answer: C
Step-by-step explanation:
10
The following table shows Edward's bank account for the month of May.
Date
Deposit Withdrawal Balance
May 2nd
$1,000
$1,000
May 9th
$250
$750
May 10th
$320
$430
May 26th
$10
$
May 27th
$500
$
Determine the account balance on May 26th and May 27th.
How much were the net withdrawals for the month of May?
dollars.
Answer: 440 dollars and -60
Step-by-step explanation:
Add ten to 430 and you’ll get 440. With a withdrawal of 500 and a balance of 440, the answer will be a negative 60 dollars.
What is the slope passing through the lines (-2,-1) (5,-4)
Answer:
-3/7 or −0.428571428571
Step-by-step explanation:
subtract -4 - -1 and 5 - -2
y1 - x1 / y2 - x2
A manufacturer produced soda cans and a quality control worker randomly selects two cans from the assembly line for testing. Past statistics show that 8% of the cans are defective. What is the probability that the two cans are defective if the quality control worker selects the two cans from a batch of 50 cans?
Step-by-step explanation:
✔️✔️✔️✔️✔️✔️✔️✔️✔️✔️✔️✔️✔️✔️✔️✔️
And ice cream stand sold $1600 worth of ice cream on Saturday which was four times the amount sold on Friday how much money did the ice cream man collect on Friday no
Answer:
$400
Step-by-step explanation:
Saturday: $1600, 4 times the amount of Friday
Friday: 1/4 the amount of Saturday
Friday: 1/4 * $1600 = $400
5. You buy a hot dog for $1.19 and a water for $0.65. Part A: What is the total price of your lunch? Part B: Use the grid below to model how much you spent:
Answer:
part A is 1.84
Step-by-step explanation:
Answer:
$1.84
Step-by-step explanation:
you line up the two items and add them together:
1
1 . 1 9
+ 0. 6 5
------------------
1 . 8 4
An office will increase salary to its top 8% employees on the basis of a performance score the office created for each employee. The performance score is approximately normal with mean 82.5 and standard deviation 9.25. How high must an employee score in order to qualify for increase in the salary?
Answer:
An employee's score in order to qualify for increase in the salary must be higher than 95.45.
Step-by-step explanation:
Let X represent the performance score of employees.
It is provided that X follows a normal distribution with parameters μ = 82.5 and σ - 9.25.
It is provided that the office will increase salary of its top 8% employees on the basis of a performance score the office created for each employee.
That is, the probability to qualify for increase in the salary is,
P (X > x) = 0.08
⇒ P (X < x) = 0.92
⇒ P (Z < z) = 0.92
The corresponding z-value is,
z = 1.40
Compute the value of x as follows:
[tex]z=\frac{x-\mu}{\sigma}\\\\1.40=\frac{x-82.5}{9.25}\\\\x=82.5+(1.40\times 9.25)\\\\x=95.45[/tex]
Thus, an employee's score in order to qualify for increase in the salary must be higher than 95.45.
64 1 x dx 0 Maple Generated Plot At least one of the limits of integration is not finite. The integrand is not continuous on [0, 64]. Determine whether it diverges or converges. converges diverges Evaluate the integral if it converges. (If the quantity diverges, enter DIVERGES.) 7 Incorrect: Your answer is incorrect.
Answer:
hello your question is incomplete attached below is the complete question
answer : The Integrand converges
Step-by-step explanation:
attached below is the detailed solution to the problem
i) the integrand is not continuous on [ 0, 64 ] hence the integrand is improper
ii) determine if the integrand diverges or converges ( attached below )
The integrand is finite and it converges at 16
Solve for x.
4x + 2
62°
680
A) 6
C) -8
B) 12
D) 8
If 173 is a prime number, what must one of its factors be?
O 173
17
37
3
Answer:
173
Step-by-step explanation:
The factors are 173 and 1.
Jim earned $95 after working days. At this rate how many days will it take him to earn $285?
Answer:
3 days.
Step-by-step explanation:
All you need to do is take th amout you want to o have by the end of a period and divide it by hw much they make in one day.
What is the unit rate for $320 for 18 ft squared to the nearest hundredth?
A school district raises $7 a day by placing an ad on a school bus. If the ad runs 5 days a week for 39 weeks, how much money will the ad raise for the school district?
A$1,365
B$2,730
C$1,540
D$1,955
Answer:
It's probably 1,365
Step-by-step explanation:
I just had that question and when I found out no one answered then I guessed and it just said "wonderful!" so that's most likely the answer
IF YOU ANSWER THIS I WILL LOVE YOU FOREVER! Which expression is equivalent to this equation?
Answer:
It's either A or B but im not sure which one
Step-by-step explanation:
If, in a random sample of items, are defective, what is the sample proportion of defective items?
Complete Question:
If in a random sample of 400 items, 88 are defective, what is the sample proportion of defective items?
Answer:
22%
Step-by-step explanation:
Given
[tex]x = 88[/tex]
[tex]n = 400[/tex]
Required
Determine the sample proportion, p
p is calculated using the following formula
[tex]p = \frac{x}{n}[/tex]
Substitute values for x and n
[tex]p = \frac{88}{400}[/tex]
[tex]p = 0.22[/tex]
Convert to percentage
[tex]p = 0.22 * 100\%[/tex]
[tex]p = 22\%[/tex]
Hence, the proportion of defective items is 22%
What are the solutions to the equation (2x - 5)(3x – 1) = 0?
O x=-ž or x = -1
O ž
O x=b or x = 1
O x = 5 or x = 3
O x = 5 or x = 1
Step-by-step explanation:
6x²-2x-15x+5=0
6x²-17x+5=0
[tex]x = \frac{17 + - \sqrt{ {17}^{2} - 4 \times 6 \times 5 } }{2 \times 6} [/tex]
[tex]x = \frac{17 + - 13}{12} [/tex]
x1= 5/2 x2= 1/3
The solutions of the given equation (2x-5)(3x-1)=0 are x=5/2 or x=1/3.
The given equation is (2x-5)(3x-1)=0.
Here, 2x(3x-1)-5(3x-1)=0
6x²-2x-15x+5=0
6x²-17x+5=0
(2x-5)(3x-1)=0
(2x-5)=0 or (3x-1)=0
2x=5 or 3x=1
Solution of quadratic equations are x=5/2 or x=1/3
Therefore, the solutions of the given equation are x=5/2 or x=1/3.
To learn more about the solution of quadratic equation visit:
https://brainly.com/question/18305483.
#SPJ7
Write the equation of the line in slope-intercept form, if the slope is 12 and the point it passes through is (2,-4) *
A. y=12x+28
B.y=12x-28
C.y=12x-20
D.y=12x
A car is traveling at a constant speed.It travels 3 1/2 miles in 5 1/4 minutes. How many minutes will it take the car to travel 70 miles
Answer:
The answer is 122 1/2 minutes.
Step-by-step explanation:
I got this answer by first subtracting 5.25-3.50=1.75 and that was how many minutes it took per mile then I multiplied 1.75x70=122.50 to get my answer.
If my answer is wrong im sorry this is my first one on this site.
Which whole number property is repersebted
Answer:
Step-by-step explanation:
In mathematics, whole numbers are the basic counting numbers 0, 1, 2, 3, 4, 5, 6, … and so on. 17, 99, 267, 8107 ,and 999999999 are examples of whole numbers. Whole numbers include natural numbers that begin from 1 onwards. Whole numbers include positive integers along with 0.
Write an equation in standard form for the line with a slope of 7 that passes through the point (1, 2).
Answer:
y=7x+2
please someone correct this if I'm wrong :D
EDIT: THIS IS SLOPE INTERCEPT FORM IM SORRYY
Step-by-step explanation:
y=mx+b
y=7x+b
y=7x+2
2 is the y in (1,2), y intercept
A car is moving at an acceleration of 20 m/s^2 and hits a wall with a force of 400 N. What is the mass of the car?
i dont know the answer but i know in the end ill get free points.
Answer:
Acceleration = change in velocity/change in time, a = (vf - vi)/t [Units: m/s/s or m/s2] .. Example: A car collides with an insect. If the car exerts a force of 10N on the insect what ... a level sidewalk at a constant speed of 1m/s if the frictional force is 400N? ... d) When the stick is hit slowly string 2 breaks because of the inertia of mass M.
Study the area model.
Which multiplication equation could represent the area model?
5.03 x 2.02 = 10.16
3.05 * 2.02 = 6.16
2.2 x 5.3 = 11.66
2.2 x 3.5 = 7.7
A triangle has side lengths measuring 20 cm, 5 cm, and n cm. Which describes the possible values of n?
0 5 < n < 15
x
O5
0 15
0 15 < n < 25
Answer: D 15 < n < 25
In triangleJKL, If angle J is seven less than angle L and angle k is 21 less than twice angle l, find the measure
of each angle.
Answer:
J=35 K=63 L=42
Step-by-step explanation:
Convert 54 2/7 to a fraction in lowest term and please work the problem out for me so I can understand how you got the answer thank you
Answer: 19/35
1) Put it over 100.
(54 2/7)/100
2)Simplify
(54 2/7)/100 = 19/35
[tex]54(\frac{2}{7})[/tex]% can be converted into a fraction of [tex]\frac{19}{140}[/tex].
What is a fraction?"A fraction represents a part of a whole or, more generally, any number of equal parts."
The given percentage of the number is
[tex]= 54(\frac{2}{7})[/tex]%
[tex]= \frac{380}{(7)(100)}[/tex]
[tex]= \frac{19}{7(20)}[/tex]
[tex]= \frac{19}{140}[/tex]
Therefore, the required fraction is [tex]\frac{19}{140}[/tex]
Learn more about fraction here: https://brainly.com/question/8482939
#SPJ3