Question

1. Suppose the amount spent on cell phone service for students per month is normally distributed and has a mean of $54 and a standard deviation of $9.

Binomial or Normal?

1. 1. What is the probability that the monthly cell phone bill for a randomly selected Wake Tech student is more than $60?
2. 2. What is the probability that the monthly cell phone bill for a randomly selected Wake Tech student is less than $50?
3. 3. Most student’s bill will be in the middle 95%. What is the lowest and highest bill for the middle 95%?

Answer 1

Normal distribution: P(X < A) = P(Z < (A - mean)/standard deviation)

Mean = $54

Standard deviation = $9

a) P(X > 60) = 1 - P(X < 60)

= 1 - P(Z < (60 - 54)/9)

= 1 - P(Z < 0.67)

= 1 - 0.7486

= 0.2514

b) P(X < 50) = P(Z < (50 - 54)/9)

= P(Z < -0.44)

= 0.3300

c) Let the lowest bill be L and highest bill be H

P(X < L) = (1-0.95)/2 = 0.025

P(Z < (L - 54)/9) = 0.025

Take Z score corresponding 0.025 from standard normal distribution table

(L - 54)/9 = -1.96

L = -1.96x9+54 = $36.36

H = 1.96x9+54 = $71.64

The lowest and highest bill for the middle 95% is $36.36 and $71.64