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10th Edition

Ron Larson

Publisher: Cengage Learning

ISBN: 9781305860919

Chapter 9, Problem 37RE

Textbook Problem

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**Waiting Time** The waiting time *t* (in minutes) for patients arriving at a health clinic is described by the probability density function

Find the probability that a patient will wait (a) no more than 5 minutes and (b) between 9 and 12 minutes.

**(a)**

To determine

**To calculate:** The probability that the patient will not wait more than 5 minutes at the health clinic for the waiting time defined by the probability density function

**Given Information:**

The probability density function of the waiting time for the patients who arrive at a health clinic is defined as,

Here, *t* is the waiting time in minutes.

**Formula used:**

If *f* is function of a continuous random variable *x*, then the probability that *x* lies in the interval

Integration formula,

Where, *C* is a constant and *a* is a real number.

The Fundamental theorem,

**Calculation:**

Consider the provided probability density function of the waiting time for the patients who arrive at a health clinic defined as,

The required probability that the patient will not wait more than 5 minutes is

Use the formula

**(b)**

To determine

**To calculate:** The probability that the patient waits between 9 and 12 minutes at the health clinic for the waiting time defined by the probability density function

Calculus: An Applied Approach (MindTap Course List)

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