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10th Edition

Ron Larson

Publisher: Cengage Learning

ISBN: 9781305860919

Chapter 9, Problem 38RE

Textbook Problem

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**Medicine** The time *t* (in days) until recovery after a certain medical procedure is described by the probability density function

Find the probability that a patient will take (a) no more than 6 days to recover and (b) at least 8 days to recover.

**(a)**

To determine

**To calculate:** The probability that the patient will not take no more than 6 days to recover after a certain medical procedure where the time until recovery is defined by the probability density function

**Given Information:**

The probability density function of the time until recovery after a certain medical procedure is defined as,

Here, *t* is the time until recovery in days.

**Formula used:**

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

The integration formula,

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

The Fundamental theorem,

**Calculation:**

Consider the provided probability density function of the time until recovery after a certain medical procedure defined as,

The required probability that the patient will take no more than 6 days to recover is

Use the formula

**(b)**

To determine

**To calculate:** The probability that the patient will take at least 8 days to recover after a certain medical procedure where the time until recovery is defined by the probability density function

Calculus: An Applied Approach (MindTap Course List)

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