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10th Edition

Ron Larson

Publisher: Cengage Learning

ISBN: 9781305860919

Chapter 9, Problem 59RE

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 mean and standard deviation of the random variable *x* which is the daily demand (in hundreds of pounds) for a certain product with the probability density function

**Given Information:**

The daily demand *x* for a certain product is defined by the probability density function,

**Formula used:**

For any probability density function *f* of a continuous random variable *x* over the interval *x* is defined as,

For any probability density function *f* of a continuous random variable *x* over the interval *x* is defined as,

Here,

**Calculation:**

Consider the provided probability density function of the daily demand.

Use the formula

Further solve,

Thus, the mean of the demand is 4 pounds.

Now, calculate the standard deviation of the demand. So, first calculate variance of the demand.

Now use the formula

Multiply the polynomials and combine like terms

**(b)**

To determine

**To calculate:** The median of the random variable *x* which is the daily demand (in hundreds of pounds) for a certain product with the probability density function

**(c)**

To determine

**To calculate:** The probability that the demand is within one standard deviation of the mean of the daily demand (in hundreds of pounds) for a certain product with the probability density function

Calculus: An Applied Approach (MindTap Course List)

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