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

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

Step-by-step 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

so firstly, we need to isolate the y variables to be able to solve these inequalities. firstly, add 0.5x on both sides of the first inequality and subtract 1.5x on both sides of the second inequality:

now since the slope is positive for the first inequality, this means that the line going upwards belongs to the first inequality, and the line going downwards belongs to the second inequality.

next, since y ≥ in the first inequality, this means that the shaded region will be above the first inequality's line, thus shading regions a and b.

next, since y ≤ in the second inequality, this means that the shaded region is going to be below this line, thus shading regions a and c.

since both lines shade region a, this means that region a is the solution.

step-by-step explanation:

mark brainliest!