Professor Ivy collects data on the time it takes for Ivy Tech students to travel to school. She find that she can model the data with the normal distribution. The mean commute time is 27.5 minutes with a standard deviation of 5.2 minutes. Based on this data, how many students out of 500 would expect their commute time to be less than 22.3 minutes?

The expected number of students is 79

Step-by-step explanation:

She find that she can model the data with the normal distribution. The formula for normal distribution is expressed as

z = (x - u) / s

Where

x = the time it takes for Ivy Tech students to travel to school.

u = mean time

s = standard deviation

From the information given,

u = 27.5 minutes

s = 5.2 minutes

The probability that a student's commute time would be less than 22.3 minutes is expressed as

P (x lesser than 22.3)

For x = 22.3

z = (22.3 - 27.5) / 5.2 = - 1

Looking at the normal distribution table, the corresponding value for a z score of - 1 is 0.15866

The number if students out of 500 whose commute time would be less than 22.3 minutes would be

0.15866 * 500 = 79