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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 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
MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
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Problem 1P
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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
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
Step 1

Given,

Population mean is 64

Standard deviation is 15

sample size = 6

 

 

Step 2

a) X~N(μ = 64, σ = 15)

 

b) The mean of the sample is same as population mean

xbar = μ = 64

The standard deviation of the sample mean is the standard error of sampling distribution:

SE = σ/n

     = 15/6

     = 6.1237

x¯ ~ N(μx = 64, σx = 6.1237)

 

 

Step 3

c)

P(55.9<X<64.5) = P[(55.9-μ)/σ < x-μσ < (64.5-μ)/σ]

                          = 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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