Answer:
10 to the 1st power
Step-by-step explanation:
531 x 10 = 5310
What is the dominan of the function f(x)= -6x+7
Answer:
(-∞,∞)
Step-by-step explanation:
It's just a line
Answer:
INFINITIE, INFINITIE
Step-by-step explanation:
what is the equation of the graph that represents the parent function f(x) = x4 stretched vertically by a factor of 2, and then shifted down 3 spaces
Answer:
f(x) = 2x^4 - 3
Step-by-step explanation:
First multiplying by 2 giving f(x) = 2x^4 stretches it vertically by factor 2.
Then subtract 3 to move it down 3 units:
f(x) = 2x^4 - 3.
Answer:
g(x)=2x^4-3
Step-by-step explanation:
Marie bought 5 1/2 gallons of paint. She uses 1/3 of the paint for a bedroom. How many gallons of paint did Marie use?
Answer:
1 5/6 gallons
Step-by-step explanation:
1. 5 1/2 = 11/2 gallons
2. She uses: 1/3 x 11/2 = 11/6 gallons
3. so: 11/6 = 1 5/6 gallons
I'M MARIE!!!
What does the graph of f(x)=(x-3)^2+12 look like
Answer:
see attached for a graph
Step-by-step explanation:
When g(x) is transformed to
f(x) = f(x -h) +k
The graph of g(x) is translated h units right and k units up.
__
Here, the function g(x) = x^2 is transformed to ...
f(x) = g(x -3) +12 = (x -3)^2 +12
Then the graph of f(x) is the graph of g(x)=x^2 translated 3 units right and 12 units up.
What’s the correct answer for this question?
Answer: choice A
Step-by-step explanation:
The shaded area represents the complement of B.
Bc or B’ is the complement of B and B’=1-B or B’=S-B
The probability that Events A and B occur is the probability of the intersection of A and B. The probability of the intersection of Events A and B is denoted by P(A ∩ B), which in this example would be equal to B.
The probability that Events A or B occur is the probability of the union of A and B. The probability of the union of Events A and B is denoted by P(A ∪ B), which in this example is equal to S.
The point A(5, -2) has been transformed to A'(-5, 2). The transformation is described as ______.
Answer:The transformation is described as a rotation of 180 degrees clockwise around the origin.
Step-by-step explanation:
I don’t understand? Please help!
6th grade math help me ! :D...
Answer: D) 180 Minutes
Step-by-step explanation:
If every hour is equal to 60 minutes and the movie (Lord of the Rings) was 3 hours longs...then we just have to multiply....
60 x 3 = 180
I hope this helps!
..........................
Answer:
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Recently, the average amount of time to foreclose on a house in the U.S. was reported to be 359 days. Assume that the standard deviation for this population is 90.4 days. A random sample of 42 homes that have completed the foreclosure process was selected. What is the probability that the sample average was less than 375 days?
Answer:
87.49% probability that the sample average was less than 375 days
Step-by-step explanation:
To solve this question, we need to understand the normal probability distribution and the central limit theorem.
Normal probability distribution
Problems of normally distributed samples are solved using the z-score formula.
In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the zscore of a measure X is given by:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.
Central Limit Theorem
The Central Limit Theorem estabilishes that, for a normally distributed random variable X, with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean [tex]\mu[/tex] and standard deviation [tex]s = \frac{\sigma}{\sqrt{n}}[/tex].
For a skewed variable, the Central Limit Theorem can also be applied, as long as n is at least 30.
In this question, we have that:
[tex]\mu = 359, \sigma = 90.4, n = 42, s = \frac{90.4}{\sqrt{42}} = 13.95[/tex]
What is the probability that the sample average was less than 375 days?
This is the pvalue of Z when X = 375. So
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
By the Central Limit Theorem
[tex]Z = \frac{X - \mu}{s}[/tex]
[tex]Z = \frac{375 - 359}{13.95}[/tex]
[tex]Z = 1.15[/tex]
[tex]Z = 1.15[/tex] has a pvalue of 0.8749.
87.49% probability that the sample average was less than 375 days
The Aluminum Association reports that the average American uses 56.8 pounds of aluminum in a year. A random sample of 49 households is monitored for one year to determine aluminum usage. If the population standard deviation of annual usage is 12.2 pounds, what is the probability that the sample mean will be each of the following?
a. More than 59 pounds
b. More than 56 pounds
c. Between 56 and 57 pounds
d. Less than 53 pounds
e. Less than 49 pounds
Answer:
a) 10.38% probability that the sample mean will be more than 59 pounds.
b) 67.72% probability that the sample mean will be more than 56 pounds.
c) 22.10% probability that the sample mean will be between 56 and 57 pounds.
d) 1.46% probability that the sample mean will be less than 53 pounds.
e) 0% probability that the sample mean will be less than 49 pounds.
Step-by-step explanation:
To solve this question, we need to understand the normal probability distribution and the central limit theorem.
Normal probability distribution
Problems of normally distributed samples are solved using the z-score formula.
In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the zscore of a measure X is given by:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.
Central Limit Theorem
The Central Limit Theorem estabilishes that, for a normally distributed random variable X, with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean [tex]\mu[/tex] and standard deviation [tex]s = \frac{\sigma}{\sqrt{n}}[/tex].
For a skewed variable, the Central Limit Theorem can also be applied, as long as n is at least 30.
In this question, we have that:
[tex]\mu = 56.8, \sigma = 12.2, n = 49, s = \frac{12.2}{\sqrt{49}} = 1.74285[/tex]
a. More than 59 pounds
This is 1 subtracted by the pvalue of Z when X = 59. So
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
By the Central Limit Theorem
[tex]Z = \frac{X - \mu}{s}[/tex]
[tex]Z = \frac{59 - 56.8}{1.74285}[/tex]
[tex]Z = 1.26[/tex]
[tex]Z = 1.26[/tex] has a pvalue of 0.8962.
1 - 0.8962 = 0.1038
10.38% probability that the sample mean will be more than 59 pounds.
b. More than 56 pounds
This is 1 subtracted by the pvalue of Z when X = 56. So
[tex]Z = \frac{X - \mu}{s}[/tex]
[tex]Z = \frac{56 - 56.8}{1.74285}[/tex]
[tex]Z = -0.46[/tex]
[tex]Z = -0.46[/tex] has a pvalue of 0.3228.
1 - 0.3228 = 0.6772
67.72% probability that the sample mean will be more than 56 pounds.
c. Between 56 and 57 pounds
This is the pvalue of Z when X = 57 subtracted by the pvalue of Z when X = 56. So
X = 57
[tex]Z = \frac{X - \mu}{s}[/tex]
[tex]Z = \frac{57 - 56.8}{1.74285}[/tex]
[tex]Z = 0.11[/tex]
[tex]Z = 0.11[/tex] has a pvalue of 0.5438
X = 56
[tex]Z = \frac{X - \mu}{s}[/tex]
[tex]Z = \frac{56 - 56.8}{1.74285}[/tex]
[tex]Z = -0.46[/tex]
[tex]Z = -0.46[/tex] has a pvalue of 0.3228.
0.5438 - 0.3228 = 0.2210
22.10% probability that the sample mean will be between 56 and 57 pounds.
d. Less than 53 pounds
This is the pvalue of Z when X = 53.
[tex]Z = \frac{X - \mu}{s}[/tex]
[tex]Z = \frac{53 - 56.8}{1.74285}[/tex]
[tex]Z = -2.18[/tex]
[tex]Z = -2.18[/tex] has a pvalue of 0.0146
1.46% probability that the sample mean will be less than 53 pounds.
e. Less than 49 pounds
This is the pvalue of Z when X = 49.
[tex]Z = \frac{X - \mu}{s}[/tex]
[tex]Z = \frac{49 - 56.8}{1.74285}[/tex]
[tex]Z = -4.48[/tex]
[tex]Z = -4.48[/tex] has a pvalue of 0.
0% probability that the sample mean will be less than 49 pounds.
What’s the correct answer for this question?
Answer:
B.
Step-by-step explanation:
Volume of the model of moon = 4/3(πr³)
= 4/3(π)(1)³
= 4.2 feet³
Volume of cylinder = πr²h
= (3.14)(0.5)²(0.5)
= 0.39 feet³
Cylindrical clay boxes to be used = 4.2/0.39
=10.7 ≈ 11
The graph of f(x) is reflected across the x-axis. Write a function g(x) to describe the new graph. g(x)=
Answer: g(x) = -f(x)
Step-by-step explanation:
When we have a point (x, y) and we reflect it over the x-axis, the end result of the reflection is the point (x, -y)
In this case we have a function reflected, and we know that we can write a function as (x, f(x))
So when we reflect it, the result will be (x, g(x)) = (x, -f(x))
So we have g(x) = -f(x)
The sum of three consecutive even integers is 186. Find the Integers.
Answer:
60, 62, 64
Step-by-step explanation:
Let x, (x + 2) & (x+ 4) be three consecutive even integers.
[tex] \therefore \: x + (x + 2) + (x + 4) = 186 \\ \therefore \:3x + 6 = 186 \\ \therefore \:3x = 186 - 6 \\ \therefore \:3x = 180 \\ \therefore \:x = \frac{180}{3} \\ \therefore \:x = 60 \\ \implies \\ x + 2 = 60 + 2 = 62 \\ x + 4 = 60 + 4 = 64[/tex]
Hence, the three consecutive even integers are 60, 62 and 64.
Researchers at a lake have determined that the percentage of fish in the lake that are intolerant to pollution can be estimated by the function
P(W,R,A)= 49-1.61W-1.41R-1.38A
where W is the percentage of wetland, R is the percentage of residential area, and A is the percentage of agricultural area surrounding the lake. Answer the questions below.
1.Use this function to estimate the percentage of fish that will be intolerant to pollution if 3 percent of the land is classified as wetland, 15 percent is classified as residential, and 0 percent is classified as agricultural.
(Note: The land can also be classified as forest land.)
2. What is the maximum percentage of fish that will be intolerant to pollution?
3. Which variable has the greatest influence on P W, R, or A
Answer:
a. 23.02 %
b. 49%
c. W
Step-by-step explanation:
Solution:-
- A multi-variable function for the percentage of fish in the lake that are intolerant to the pollution is given as:
[tex]P ( W , R , A ) = 49 - 1.61W - 1.41R - 1.38A[/tex]
Where,
W: percentage of wetland
R: percentage of residential area
A: percentage of agriculture
- We are to evaluate the percentage of fish intolerant to pollution in the case where W = 3 , R = 15 , A = 0. We will plug in the values in the modeled function P ( W , R , A ) as follows:
[tex]P ( 3 , 15 , 0 ) = 49 - 1.61*3 - 1.41*15 -1.38*0\\\\P ( 3 , 15 , 0 ) = 23.02\\[/tex]
- To determine the maximum percentage of fish that will be intolerant to pollution we will employ the use of critical points. The critical point that is defined by the linear relationship between P and all other parameters ( W, R , A ). The maximum value occurs when W = R = A = 0.
[tex]P ( 0 , 0 , 0 ) = 49 - 1.61*0 -1.41*0 - 1.38*0 = 49[/tex]
- Hence, the maximum value of the function is 49%.
- The linear relationship between each induvidual parameter ( R, W , A ) and the function ( P ) is proportional in influence. The extent of influence can be quantized by the constant multiplied by each parameter.
- We see that that ( 1.61*W ) > ( 1.41R ) > ( 1.38A ). The greatest influence is by parameter ( W ) i.e the influence of percentage of wetlands .
6(a–1.4)=3.5a+1.6
Please answer fast!
Confidence Interval Concept Check 3 1 point possible (graded) In a new experiment consisting of 150 couples, 75 couples are observed to turn their heads to the left and the remaining 75 couples turned their heads to the right when kissing. Let p denote the (unknown) parameter which specifies the probability that a couple turns their head to the right.
Which of the following statements are correct regarding this experiment? You are given that exactly one but not both of choices 3 and 4 is correct. Also, assume that the given confidence intervals are an instance of a random interval computed upon observing the given data.
10,05] is a 50% asymptotic confidence interval for p. [0.5, 1] is a 50% asymptotic confidence interval for p. 10.466, 0.533 is a 50% asymptotic confidence interval for p. 10.48, 0.52 is a 50% asymptotic confidence interval for p. O
Answer:
Step-by-step explanation:
There are four options given above.
P specifies the probability that a couple turns their head to the right when kissing. P is 0.5 because the probability of turning right when kissing is 75÷150 = 1/2 = 0.5
Assuming that the given confidence intervals are an instance of a random interval computed upon observing the given data,
The correct statements are statements 1 and 4
Gasoline is that distillation fraction that has a boiling point range of
Answer:
Gasoline is a petroleum-derived product comprising a mixture of liquid aliphatic and aromatic hydrocarbons, ranging between C4 and C12 carbon atoms with the boiling range of 30–225°C. It is predominantly a mixture of paraffins, naphthenes, aromatics and olefins. hope that helps love!
Answer:
Answer is below
Step-by-step explanation:
Gasoline has an initial boiling point at about 35 °C or 95 °F and a final boiling point of about 200 °C or 395 °F.
A researcher is investigating a government claim that the unemployment rate is less than 5%. To test this claim, a random sample of 1500 people is taken and its determined that 92 people are unemployed. The following is the setup for this hypothesis test:
H0:p=0.05 Ha:p<0.05
Required:
Find the test statistic for this hypothesis test for a proportion. Round your answer to 2 decimal places.
Answer:
[tex]\hat p=\frac{92}{1500}=0.0613[/tex] estimated proportion of unemployed
[tex]z=\frac{0.0613 -0.05}{\sqrt{\frac{0.05(1-0.05)}{1500}}}=2.01[/tex]
Step-by-step explanation:
Information given
n=1500 represent the random sample taken
X=92 represent the number of people unemployed
[tex]\hat p=\frac{92}{1500}=0.0613[/tex] estimated proportion of unemployed
[tex]p_o=0.05[/tex] is the value to value to test
z would represent the statistic
[tex]p_v[/tex] represent the p value
System of hypothesis
We want to test if the true proportion is lower than 0.05 or no and the system of hypothesis are::
Null hypothesis:[tex]p \geq 0.5[/tex]
Alternative hypothesis:[tex]p < 0.5[/tex]
The statistic is given by:
[tex]z=\frac{\hat p -p_o}{\sqrt{\frac{p_o (1-p_o)}{n}}}[/tex] (1)
Replacing the info given we got:
[tex]z=\frac{0.0613 -0.05}{\sqrt{\frac{0.05(1-0.05)}{1500}}}=2.01[/tex]
Sam is rowing a boat away from a dock. The graph shows the relationship
between time and Sam's distance from the dock. Evaluate the function for an
input of 6.
Distance from Dock
130
100
90
90
20
CO
Distance (meters)
Times (minutes)
2(v-1) + 8 = 6(2v -4)
Choose statement that solves the solution
Answer:
V=3
Step-by-step explanation:
2(v-1)+8=6(2v-4)
2V-2+8=12v-24(calculate)
2v+6=12v-24(move terms)
2v-12v=-24-6(collect like terms)
-10v=-30(devide both sides by-10)
V=3
hi I hope this helps.
Gale wants to buy tickets to the aquarium or the wave pool and invite some friends. He sets up a table to track the total cost for the tickets at each place to determine the best value. Use the drop-down menus to select appropriate column labels.
Column 1 label:
Column 2 label:
Column 3 label:
here are the label options
Gale
tickets
total cost for aquarium
total cost for wave pool
Answer:
This is the answer EDGE 2020
PLEASE HELP ME
Angles PTQ and STR are vertical angles and congruent.
Circle T is shown. Line segments T P, T Q, T R, and T S are radii. Lines are drawn to connect points P and Q and points S and R to create secants. Angles P T Q and R T S are congruent.
Which arcs are congruent?
Arc S P and Arc S R
Arc P Q and Arc S R
Arc P Q and Arc Q R
Arc S P and Arc P R
Answer:
PQ AND SR on ED
Step-by-step explanation:
Based on vertical angle theorem, arcs that are congruent is option (B) arc P Q and arc S R is the correct answer.
What is vertical angle theorem?The vertical angles theorem is a theorem that states that when two lines intersect and form vertically opposite angles, each pair of vertical angles has the same angle measures. A pair of vertically opposite angles are always equal to each other.
For the given situation,
Angles PTQ and STR are vertical angles and congruent.
Line segments T P, T Q, T R, and T S are radii.
So, T P = T Q = T R = T S.
The two sides T P = T Q and T R = T S and [tex]\angle PTQ = \angle RTS[/tex],
then by SAS similarity theorem two triangles,
Δ PTQ ≅ Δ STR.
When two triangles are congruent, then the corresponding arc are also congruent.
The congruent central angles intercept congruent arcs PQ and SR.
Hence we can conclude that based on vertical angle theorem, arcs that are congruent is option (B) arc P Q and arc S R is the correct answer.
Learn more about vertical angle theorem here
https://brainly.com/question/17702030
#SPJ2
In studies examining the effect of humor on interpersonal attractions, McGee and Shevlin (2009) found that an individual’s sense of humor had a significant effect on how the individual was perceived by others. In one part of the study, female college students were given brief descriptions of a potential romantic partner. The fictitious male was described positively as being single and ambitious and having good job prospects. For one group of participants, the description also said that he had a great sense of humor. For another group, it said that he has no sense of humor. After reading the description, each participant was asked to rate the attractiveness of the man on a seven-point scale from 1 (very unattractive) to 7 (very attractive). A score of 4 indicates a neutral rating. The females who read the "great sense of humor" description gave the potential partner an average attractiveness score of M = 4.53 with a standard deviation of s = 1.04. If the sample consisted of n = 16 participants, is the average rating significantly higher than neutral (μ = 4)? Use a one-tailed test with α = .05
Answer:
The calculated value t = 2.038< 2.145 at 0.05 level of significance
Null hypothesis is accepted
There is the average rate is less than μ ≤ 4
Step-by-step explanation:
Step(i):-
The Population of the mean 'μ' =4
sample size 'n' = 16
sample mean 'x⁻' = 4.53
given sample standard deviation 's' = 1.04
level of significance α = 0.05
Step(ii):-
Null hypothesis:H₀ : There is no significance difference between two means
Alternative hypothesis : H₁: There is significance difference between two means
Test statistic
[tex]t = \frac{x^{-} - mean}{\frac{S}{\sqrt{n} } }[/tex]
[tex]t = \frac{4.53-4}{\frac{1.04}{\sqrt{16} } }[/tex]
t = 2.038
Degrees of freedom ν = n-1 = 16-1 =15
t₀.₀₂₅ = 2.145
Conclusion:-
The calculated value t = 2.038< 2.145 at 0.05 level of significance
Null hypothesis is accepted
There is the average rate is less than μ ≤ 4
My fourth number is 39 my fifth number is 43 what is my first number ?
Answer:
27
Step-by-step explanation:
39+4=43
27, 31, 35, 39, 43
Answer:
27
Step-by-step explanation:
When you add u subtract 39 from 43 u will get 4
Therefore u will subtract 4 from 39 to get the third number which is 35 then subtract 4 from it to get the second number which is 31 then subtract another 4 to get the first number that's 27
A jar of candy has 6 cinnamon, 5 peppermint and 7 spearmint candies in it. Your pick five pieces of candy out of the jar at the same time. What is the probability that three are cinnamon and two are peppermint?
Answer:
2.33% probability that three are cinnamon and two are peppermint
Step-by-step explanation:
A probability is the number of desired outcomes divided by the number of total outcomes.
The order in which the candies are chosen is not important. So we use the combinations formula to solve this question.
Combinations formula:
[tex]C_{n,x}[/tex] is the number of different combinations of x objects from a set of n elements, given by the following formula.
[tex]C_{n,x} = \frac{n!}{x!(n-x)!}[/tex]
Desired outcomes:
3 cinnamon, from a set of 6.
2 peppermint, from a set of 5. So
[tex]D = C_{6,3}*C_{5,2} = \frac{6!}{3!(6-3)!}*\frac{5!}{2!(5-2)!} = 200[/tex]
Total outcomes:
5 candies, from a set of 6+5+7 = 18. So
[tex]T = C_{18,5} = \frac{18!}{5!(18-5)!} = 8568[/tex]
Probability:
[tex]p = \frac{D}{T} = \frac{200}{8568} = 0.0233[/tex]
2.33% probability that three are cinnamon and two are peppermint
express 1)32.12353535... 2)2.3333...+4.15151515... as a fraction in simplest form
(1) Suppose x = 32.12353535... . Then 100x = 3212.353535... and 10000x = 321235.353535... .
Subtracting these gives
10000x - 100x = 321235.353535... - 3212.353535...
9900x = 321235 - 3212
9900x = 318023
x = 318023/9900
(2) By the same process as above, we start with
x = 2.333...
y = 4.151515...
Then
10x = 23.333...
==> 10x - x = 23.333... - 2.333...
==> 9x = 23 - 2
==> x = 21/9
and
100y = 415.151515...
==> 100y - y = 415.151515... - 4.151515
==> 99y = 415 - 4
==> y = 411/99
After this, we get
x + y = 2.333... + 4.151515...
==> x + y = 21/9 + 411/99
==> x + y = 231/99 + 411/99
==> x + y = 642/99 = 214/33
Which of the following pairs of lines are perpendicular? How do you know?
Find the largest interval which includes x = 0 for which the given initial-value problem has a unique solution. (Enter your answer using interval notation.) (x − 5)y'' + 3y = x, y(0) = 0, y'(0) = 1
Answer:
The largest interval is [tex]-\infty < 0 < 5[/tex]
Step-by-step explanation:
From the question the equation given is
[tex](x-5)y'' + 3y = x \ \ \ y(0) = 0 \ , y'(0) = 1[/tex]
Now dividing the both sides of this equation by (x-5)
[tex]y'' + \frac{3y}{(x-5)} = \frac{x}{x-5}[/tex]
Comparing this equation with the standard form of 2nd degree differential which is
[tex]y'' + P(x)y' + Q(x) y = R(x)[/tex]
We see that
[tex]Q(x) = \frac{3y}{(x-5)}[/tex]
[tex]R(x) = \frac{x}{(x-5)}[/tex]
So at x = 5 [tex]Q(x) \ and \ R(x)[/tex] are defined for this equation because from the equation of [tex]Q(x) \ and \ R(x)[/tex] x = 5 give infinity
This implies that the largest interval which includes x = 0 , P(x) , Q(x) , R(x ) is
[tex]-\infty < 0 < 5[/tex]
This because x = 5 is not defined in y domain
The length of human pregnancies from conception to birth is normally distributed with mean 266 days and standard deviation 16 days. What is the proportion of the lengths of pregnancies that fall between 250 days and 282 days?
Please put the answer in the standard deviation percentages!
Answer:
68% of the lengths of pregnancies fall between 250 days and 282 days.
Step-by-step explanation:
The Empirical Rule states that, for a normally distributed random variable:
68% of the measures are within 1 standard deviation of the mean.
95% of the measures are within 2 standard deviation of the mean.
99.7% of the measures are within 3 standard deviations of the mean.
In this problem, we have that:
Mean = 266
Standard deviation = 16.
What is the proportion of the lengths of pregnancies that fall between 250 days and 282 days?
250 = 266 - 16
So 250 is one standard deviation below the mean.
282 = 266 + 16
So 282 is one standard deviation above the mean.
By the Empirical Rule, 68% of the lengths of pregnancies fall between 250 days and 282 days.
Answer:
[tex]P(250<X<282)=P(\frac{250-\mu}{\sigma}<\frac{X-\mu}{\sigma}<\frac{282-\mu}{\sigma})=P(\frac{250-266}{16}<Z<\frac{282-266}{16})=P(-1<z<1)[/tex]
And we can find this probability with this difference and using the normal standard table or excel:
[tex]P(-1<z<1)=P(z<1)-P(z<-1)= 0.8413-0.1587= 0.6826[/tex]
So then we will have approximatetly 68.26% of the values between 250 and 282 days
Step-by-step explanation:
Let X the random variable that represent the The length of human pregnancies from conception to birth, and for this case we know the distribution for X is given by:
[tex]X \sim N(266,16)[/tex]
Where [tex]\mu=266[/tex] and [tex]\sigma=16[/tex]
We are interested on this probability
[tex]P(250<X<282)[/tex]
And the best way to solve this problem is using the normal standard distribution and the z score given by:
[tex]z=\frac{x-\mu}{\sigma}[/tex]
If we apply this formula to our probability we got this:
[tex]P(250<X<282)=P(\frac{250-\mu}{\sigma}<\frac{X-\mu}{\sigma}<\frac{282-\mu}{\sigma})=P(\frac{250-266}{16}<Z<\frac{282-266}{16})=P(-1<z<1)[/tex]
And we can find this probability with this difference and using the normal standard table or excel:
[tex]P(-1<z<1)=P(z<1)-P(z<-1)= 0.8413-0.1587= 0.6826[/tex]
So then we will have approximatetly 68.26% of the values between 250 and 282 days