Statistics Question: The repair cost of a Subaru engine is normally distributed with a mean of $5,850 and standard deviation of $1,125.

Question

The repair cost of a Subaru engine is normally distributed with a mean of $5,850 and standard deviation of $1,125. Random samples of 20 Subaru engines are drawn from this population and the mean repair cost of each sample is calculated. Which of the following mean costs would be considered unusual?

 

A.$6350

B.$6180

C.$5180

D. None of these 

 

 

The answer is C. But i need to figure out how to get that 

Answer 1

Given the standard deviation of the normally distributed population is 1125, we can calculate the sample error as:

1125/sqrt(n) where n=20 is the sample size.  This suggest that the standard error is 251.

 

Given this standard error a measurement of $5180 would be $670 from the mean or 2.66 standard error smaller than the mean.  This is rather unusual.  The probability of this occurring by chance is less than 0.4%.  

 

https://en.wikipedia.org/wiki/Standard_normal_table

 

Answer 2

Calculate the differences (absolute value) from the mean; you get:

A 500

B 330

C 670

 

C is the one farthest from the mean, and it's lower than the mean, so C looks like a good bargain (if the repairs are done well).  The probability of this C situation is 27.6%