Question

3. Joe the barber charges $32 for a shave and haircut and $20 for just a haircut. Based on experience,

he determines that the probability that a randomly selected customer comes in for a shave and"
haircut is 0.85, the rest of his customers come in for just a haircut. Let J= what Joe charges a
randomly selected customer.
(a) Give the probability distribution for J.
(b) find and interpret the mean of J, Mj
(c) find and interpret the standard deviation of J, standard deviation J

Answer 1

A. Give the probability distribution for J.

J 20 32

p 0.15 0.85

B. Find and interpret the mean of J, Mj

Mj = 30.2

This means that the average customer that come in spends $ 30.20 at the barber shop

C. Find and interpret the standard deviation of J, standard deviation J

sdJ = 4.28

This means that the average customer that come in could spend +/- $ 4.28 at the barber shop, from $ 25.92 to $ 34.48

Explanation:

Let's write our table of probabilities for the services provided by Joe the barber, this way:

A. Give the probability distribution for J.

J 20 32

p 0.15 0.85

B. Find and interpret the mean of J, Mj

Mj = (20 * 0.15 ) + (32 * 0.85)

Mj = 3 + 27.2 = 30.2

This means that the average customer that come in spends $ 30.20 at the barber shop

C. Find and interpret the standard deviation of J, standard deviation J

sdJ = √(20 - 30.2)² * 0.15 + (32 - 30.2)² * 0.85

sdJ = √15.606 + 2.754

sdJ = 4.28

This means that the average customer that come in could spend +/- $ 4.28 at the barber shop, from $ 25.92 to $ 34.48