Paying for music downloads. In Exercise 4.49 (p. 210) you

Chapter 4, Problem 103E

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QUESTION:

Problem 103E

Paying for music downloads. In Exercise 4.49 (p. 210) you learned that half of all U.S. adults use the Internet and have paid to download music (Pew Internet & American Life Project Survey, October 2010). In a random sample of 250 U.S. adults, let x be the number who use the Internet and pay to download music.

a. Find the mean of x. (This value should agree with your answer to Exercise 4.49c.)

b. Find the standard deviation of x. c. Find the z-score for the value x = 200.

d. Find the approximate probability that the number of the 250 adults who use the Internet and pay to download music is less than or equal to 200.

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QUESTION:

Problem 103E

Paying for music downloads. In Exercise 4.49 (p. 210) you learned that half of all U.S. adults use the Internet and have paid to download music (Pew Internet & American Life Project Survey, October 2010). In a random sample of 250 U.S. adults, let x be the number who use the Internet and pay to download music.

a. Find the mean of x. (This value should agree with your answer to Exercise 4.49c.)

b. Find the standard deviation of x. c. Find the z-score for the value x = 200.

d. Find the approximate probability that the number of the 250 adults who use the Internet and pay to download music is less than or equal to 200.

ANSWER:

Solution :

Step 1 of 4:

    From exercise 4.49. We determined that x is a binomial random variable with n = 250, p = 0.5.

      q = 1- p = 1- 0.5 = 0.5.

a). To find the mean of x.

        The mean of a binomial distribution is

              

                  = 250(.5)

                  = 125.

          Therefore, the mean of x is 125.


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