Chapter 9.3, Problem 47E

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10th Edition

Ron Larson

ISBN: 9781305860919

Textbook Problem

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**Demand** The daily demand *x* for a certain product (in hundreds of pounds) is a random variable with the probability density function

(a) Find the mean and standard deviation of the demand.

(b) Find the median of the demand.

(c) Find the probability that the demand is within one standard deviation of the mean.

**(a)**

To determine

**To calculate:** The expected value(mean) and standard deviation of the probability density function *x* as a random variable of a certain product(in hundreds of pounds).

Explanation

**Given information:**

The function is,

And the interval is

**Formula used:**

To find the expected value or mean of *x*,

The variance of *x* is,

The standard deviation of *x* is,

Where, *f* is a probability density function with a continuous random variable *x* in the interval

**Calculation:**

Consider the provided function is,

Now apply the formula

Further solve,

**(b)**

To determine

**To calculate:** The median of the probability density function *x* as a random variable of a certain product (in hundreds of pounds).

**(c)**

To determine

**To calculate:** The probability that the demand is within one standard deviation of the mean, if the probability density function *x* as a random variable of a certain product (in hundreds of pounds).

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