The average number of miles (in thousands) that a car's tire will function before needing replacement is 64 and the standard deviation is 15. Suppose that 6 randomly selected tires are tested. Round all answers to 4 decimal places where possible and assume a normal distribution. a. What is the distribution of X? X - N( 64 b. What is the distribution of æ? ¤ ~ N( c. If a randomly selected individual tire is tested, find the probability that the number of miles (in thousands) before it will need replacement is between 55.9 and 64.5. d. For the 6 tires tested, find the probability that the average miles (in thousands) before need of replacement is between 55.9 and 64.5. e. For part d), is the assumption that the distribution is normal necessary? YesO No o
The average number of miles (in thousands) that a car's tire will function before needing replacement is 64 and the standard deviation is 15. Suppose that 6 randomly selected tires are tested. Round all answers to 4 decimal places where possible and assume a normal distribution. a. What is the distribution of X? X - N( 64 b. What is the distribution of æ? ¤ ~ N( c. If a randomly selected individual tire is tested, find the probability that the number of miles (in thousands) before it will need replacement is between 55.9 and 64.5. d. For the 6 tires tested, find the probability that the average miles (in thousands) before need of replacement is between 55.9 and 64.5. e. For part d), is the assumption that the distribution is normal necessary? YesO No o
MATLAB: An Introduction with Applications
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Author:Amos Gilat
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![The average number of miles (in thousands) that a car's tire will function
before needing replacement is 64 and the standard deviation is 15. Suppose
that 6 randomly selected tires are tested. Round all answers to 4 decimal
places where possible and assume a normal distribution.
a. What is the distribution of X? X - N( 64
b. What is the distribution of ? ¤ - N(
c. If a randomly selected individual tire is tested, find the probability
that the number of miles (in thousands) before it will need
replacement is between 55.9 and 64.5.
d. For the 6 tires tested, find the probability that the average miles (in
thousands) before need of replacement is between 55.9 and 64.5.
e. For part d), is the assumption that the distribution is normal
necessary?
YesO No o](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F0017d92f-fd5a-4a34-8e16-36b3a20e3d6d%2F4a8483a7-8fe3-4120-8165-38f6be894575%2Fbxqkz57_processed.png&w=3840&q=75)
Transcribed Image Text:The average number of miles (in thousands) that a car's tire will function
before needing replacement is 64 and the standard deviation is 15. Suppose
that 6 randomly selected tires are tested. Round all answers to 4 decimal
places where possible and assume a normal distribution.
a. What is the distribution of X? X - N( 64
b. What is the distribution of ? ¤ - N(
c. If a randomly selected individual tire is tested, find the probability
that the number of miles (in thousands) before it will need
replacement is between 55.9 and 64.5.
d. For the 6 tires tested, find the probability that the average miles (in
thousands) before need of replacement is between 55.9 and 64.5.
e. For part d), is the assumption that the distribution is normal
necessary?
YesO No o
Expert Solution
![](/static/compass_v2/shared-icons/check-mark.png)
Step 1
Given,
Population mean is 64
Standard deviation is 15
sample size = 6
Step 2
a) X~N( = 64, = 15)
b) The mean of the sample is same as population mean
xbar = = 64
The standard deviation of the sample mean is the standard error of sampling distribution:
SE = /
= 15/
= 6.1237
~ N(x = 64, x = 6.1237)
Step 3
c)
P(55.9<X<64.5) = P[(55.9-)/ < < (64.5-)/]
= P[(55.9-64)/15 < Z < (64.5-64)/15]
= P(-0.54 < Z < 0.033)
= P(Z<0.033)- P(Z<-0.54)
= 0.51197 - 0.29460
= 0.21737
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