Question

Suppose that the waiting time for a pizza to be ready at a local pizzeria has been found to be normally distributed with a mean of 15 minutes and a standard deviation of 7 minutes. Suppose that in an effort to provide better service to the customers, the manager has decided to provide discounts to those individuals whose waiting time exceeds a predetermined time. The manager decides that 15% of the customers should receive this discount. What are the number of minutes they need to wait to receive the discount?

Answer 1

Answer:

If the waiting time exceeds 22.52 minutes, the customer will receive the discount.

Step-by-step explanation:

We are given the following information in the question:

Mean, μ = 15 minutes

Standard Deviation, σ = 7 minutes

We are given that the distribution of waiting time is a bell shaped distribution that is a normal distribution.

Formula:

$z_{score} = \displaystyle\frac{x-\mu}{\sigma}$

We have to find the value of x such that the probability is 0.15

P(X > x) = 0.15

$P(z>\displaystyle\frac{x-15}{7}) = 0.15\\\\1 - P(z<\displaystyle\frac{x-15}{7}) = 0.15\\\\P(z<\displaystyle\frac{x-15}{7}) = 0.85$

Calculating the value from standard normal table, we have,

$P(z<1.036) = 0.85$

Comparing, we get,

$\displaystyle\frac{x-15}{7} = 1.036\\\\x = 22.252 \approx 22.52$

If the waiting time exceeds 22.52 minutes, the customer will receive the discount.

Answer 2

The number of minutes they need to wait to receive the discount is approximately 22

Probability and normal distribution

The formula for calculating the z score is expressed as:

$z =\frac{x-\mu}{\sigma}$

Given the following parameters;

P(X > x) = 0.15

$p(z < \frac{x-15}{7})=1-0.15\\ p(z < \frac{x-15}{7})=0.85$

According to the standard table;

$p(z < 1.036)=0.85$

$\frac{x-15}{7} =1.036$

Solve the expression for the value of x

x - 15  = 7(1.036)
x - 15 = 7.252

x = 15 + 7.252
x = 22.352

Hence the number of minutes they need to wait to receive the discount is approximately 22

Learn more on normal distribution here: https://brainly.com/question/4079902