Question

The time needed to complete a final examination in a particular college course is normally distributed with a mean of 79 minutes and a standard deviation of 8 minutes. Answer the following questions. Round the intermediate calculations for z value to 2 decimal places.

1. What is the probability of completing the exam in one hour or less (to 4 decimals)?
   
2. What is the probability that a student will complete the exam in more than 60 minutes but less than 75 minutes (to 4 decimals)?
   
3. Assume that the class has 60 students and that the examination period is 90 minutes in length. How many students do you expect will be unable to complete the exam in the allotted time (to the next whole number)?

I need to understand how to do this in excel.

Answer 1

Given Data

Mean   = 79

standard deviation = 8

a) probability of completing the exam in one hour or less = P(X 60)

P(X 60) = P[ Z < ]

In excel , using excel function solver standardize function to calculate z value

=STANDARDIZE(X, , )

a) probability of completing the exam in one hour or less = P(X 60) = 0.0088

b) probability that a student will complete the exam in more than 60 minutes but less than 75 minutes P(60 < X < 75) = 0.2997

c) n = 60 x =90

p(x > 90) = 0.0846

Expected number E(X) = n*p = 60*0.0846 = 5.076 = 5