Question

v

You may need to use the appropriate appendix table to answer this question.

The time needed to complete a final examination in a particular college course is normally distributed with a mean of 80 minutes and a standard deviation of 10 minutes. Answer the following questions.

(a)

What is the probability of completing the exam in one hour or less? (Round your answer to four decimal places.)

(c)

Assume that the class has 90 students and that the examination period is 95 minutes in length. How many students do you expect will be unable to complete the exam in the allotted time? (Round your answer up to the nearest integer.)

students

Answer 1

Given,

= 80, = 10

We convert this to standard normal as

P( X < x) = P( Z < x - / )

a)

P( Z < 60) = P( Z < 60 - 80 / 10)

= P( Z < -2)

= 0.0228

b)

P( X > 95) = P( Z > 95 - 80 / 10)

= P( Z > 1.5)

= 0.0668

So, of the 90 students we expect, 90 * 0.0668 = 7 students will be unable to complete the exam in the allotted time.