Question

1. On a certain test grades are skewed to the left with a mean of 75 and a standard deviation of 5. A statistics teacher takes a sample of 64 test grades.
(A) What is the probability the mean of the 64 test grades was at least 74? (9 points)
(B) What mean separates the highest 10% of means from the rest of the means? (10 points)
Show work and excel formulas

Answer 1

Since sample n = 65 is sufficiently large ( n > 30) , central limit theorem can be used.

~ N ( , / sqrt(n) ) = N( 75 , 5 / sqrt(64)) = N ( 75 , 0.625 )  

A)

P( >= 74) = 1 - P( <= 74)

= 1 - NORM.DIST( X , mean , SD , cumulative) [ (using EXCEL)

= 1 - NORM.DIST ( 74 , 75 , 0.625 , TRUE)

= 1 - 0.0548

= 0.9452

b)

P( > x) = 0.10

P( < x) = 1 - 0.10

P( < x) = 0.90

Using EXCEL,

= NORM.INV ( Probability , mean , SD)

= NORM.INV ( 0.90 , 75 , 0.0625)

= 75.801