Answered: The patient director of Health plus…

MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

Section: Chapter Questions

Problem 1P

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Question

The patient director of Health plus clinic has just conducted a study of customer waiting time before seeing a doctor. For the study, he randomly observed 1045 patients throughout one-week. Let assume that the waiting time has an approximately normal distribution with a mean time of 22.14 and a standard deviation of 6.09. Based on this assumption, the patient director is considering providing a gift certificate to any customer required to wait more than 30 minutes.

What is the probability of having to pay off on this offer?

Suppose the patient director believes this procedure is too generous. He would like to set the time limit so that the likelihood of giving out the gift is at most only 5%.

2. What will be the required waiting time for any customer to receive a gift certificate?

Expert Solution

Step 1

Given,

n = 1045

$μ = 22.14 σ = 6.09 x = 30$

To find,

1. what is the probability of having to pay off on this offer?

Step 2

1. what is the probability of having to pay off on this offer?

Answer:

P ( X > 30)

= 1 - P (X < 30)

$= 1 - P (\frac{x - μ}{σ} < \frac{30 - 22.14}{6.09}) = 1 - P (Z < 1.29) = 1 - 0.90147 = 0.09853$

The probability of having to pay off on this offer is 0.09853.

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