Mathematics: 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

lolStep-by-step explanation:...

Suppose that the waiting time for a pizza to be

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14.01.2022

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

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

Calculating the value from standard normal table, we have,

P(z

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.

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