Question

A pizza shop delivers only one kind of pizza, which is sold for $ 10 $10dollar sign, 10, and costs the pizza shop $ 6 $6dollar sign, 6 to make. The pizza shop has a delivery policy that says if the pizza takes longer than half an hour to arrive, there is no charge. Experience has shown that delivery takes longer than half an hour only 10 % 10%10, percent of the time. Let the random variable X XX be the pizza shop's profit for a randomly selected delivery order for one of these pizzas. Here is the probability distribution for X XX: Late On-time X = profit X=profitX, equals, start text, p, r, o, f, i, t, end text − $ 6 −$6minus, dollar sign, 6 $ 4 $4dollar sign, 4 P ( X ) P(X)P, left parenthesis, X, right parenthesis 0.10 0.100, point, 10 0.90 0.900, point, 90 Calculate the mean of X XX. Μ X = μ X ​ =mu, start subscript, X, end subscript, equals dollars Show Calculator

Answer 1

Answer:

$3

Step-by-step explanation:

The probability distribution for X, the pizza shop's profit is given below:

$\left|\begin{array}{c|c|c}----&-----&----\\& Late& On-Time\\----&-----&----\\ X=Profit&-\ 6&\ 4\\----&-----&----\\P(X)&0.10&0.90\\----&-----&----\\\end{array}\right|$

The mean of X is the expected value of X.

Mean, $\mu=(0.10X-6)+(0.90X4)$

=-0.6+3.6

=$3

The mean profit of the pizza's shop for a randomly selected delivery order for one of these pizzas is $3.