Question

***PLEASE SHOW HOW TO SOLVE IN EXCEL*** NOT HANDWRITTEN

6) The time needed to complete a final examination in a particular college course is normally distributed with a mean of 90 minutes and a standard deviation of 15 minutes. Answer the following questions.

a. What is the probability of completing the exam in one hour or less?

b. What is the probability that a student will complete the exam in more than 60 minutes but less than 105 minutes?

c. Assume that the class has 60 students and that the examination period is 120 minutes in length. How many students do you expect will be unable to complete the exam in the allotted time?

Answer 1

Given Data :

Mean   = 80

standard deviation = 10

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) = 0.0228

b) probability that a student will complete the exam in more than 60 minutes but less than 105 minutes P(60 < X < 105) = 0.8186

c) n = 60 x =120

p(x > 120) = 0.0228

Expected number E(X) = n*p = 60*0.0228 = 1.368 = 1.37 = 1