Question

The distance a student lives (in miles) from their classroom is approximately normally distributed with a mean of 5 miles and a standard deviation of 1.5 miles. Use the normal table to find the probabilities.

a) How far away do the closest 15% of students live?

b) What is the probability that a student will live less than 7 miles away?

c) What is the probability that a student will live further away than 3 miles

or less than 7 miles away?

Answer 1

Answer a)

Let x miles be the value below which 15% of of students live

P(X < x) = 0.15

Let z be the z score corresponding to x.

Therefore, P(Z < z) = 0.15

z value based on standard normal table is -1.04

z = (x-μ)/σ

-1.04 = (x-5)/1.5

x = 5 - 1.04*1.5

x = 3.44

The closest 15% of students live 3.44 miles away

Answer b)

The probability that a student will live less than 7 miles away is 0.9082

Answer c)

P ( −1.33<Z<1.33 ) = P(Z<1.33) - P ( Z<-1.33) = 0.9082-0.0918

P ( −1.33<Z<1.33 ) = 0.8164

The probability that a student will live further away than 3 miles or less than 7 miles away is 0.8164