Question

A professor's commute is normally distributed with a mean of 40 minutes and a standard deviation of 10 minutes. (a) What is the probability that the professor gets to work in 30 min or less? (Round your answer to three decimal places.) . (b) If the professor has a 9 A.M. class and leaves home at 8 A.M., how often is the professor late for class? (Round your answer to one decimal place.) - % of the time

Answer 1

Solution:

Given: A professor's commute is normally distributed with a mean of 40 minutes and a standard deviation of 10 minutes.

That is: X ~ Normal distribution with Mean = and Standard Deviation =

Part a) What is the probability that the professor gets to work in 30 min or less?

That is:

P( X < 30 ) = .......?

Find z score:

P( X < 30 ) = P( Z < -1.00)

Look in z table for z = -1.0 and 0.00 and find area.

Thus we get:

P( Z < -1.00) = 0.1587

Thus

P( X < 30 ) = P( Z < -1.00)

P( X < 30 ) = 0.1587

P( X < 30 ) = 0.159

Part b) If the professor has a 9 A.M. class and leaves home at 8 A.M., how often is the professor late for class?

Number of minutes between 8 to 9 am are = 60 minutes

If he takes 60 or less minutes , then he will reach in time, if he takes more than 60 minutes , then he will be late.

Thus we have to find:

P( X > 60) = .............?

Find z score:

Thus we get:

P( X > 60) = P( Z > 2.00)

P( X > 60) =1 - P( Z < 2.00)

Look in z table for z = 2.0 and 0.00 and find area.

Thus from z table we get:

P( Z < 2.00) = 0.9772

Then

P( X > 60) =1 - P( Z < 2.00)

P( X > 60) =1 - 0.9772

P( X > 60) = 0.0228

P( X > 60) = 2.28%

P( X > 60) = 2.3%

2.3% of the time the professor late for class.