A recent CBS News survey reported that 67 percent of

Chapter 6, Problem 59E

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QUESTION:

Problem 59E

A recent CBS News survey reported that 67 percent of adults felt the U.S. Treasury should continue making pennies.

Suppose we select a sample of 15 adults.

a. How many of the 15 would we expect to indicate that the Treasury should continue making pennies? What is the standard deviation?

b. What is the likelihood that exactly 8 adults would indicate the Treasury should continue making pennies?

c. What is the likelihood at least 8 adults would indicate the Treasury should continue making pennies?

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QUESTION:

Problem 59E

A recent CBS News survey reported that 67 percent of adults felt the U.S. Treasury should continue making pennies.

Suppose we select a sample of 15 adults.

a. How many of the 15 would we expect to indicate that the Treasury should continue making pennies? What is the standard deviation?

b. What is the likelihood that exactly 8 adults would indicate the Treasury should continue making pennies?

c. What is the likelihood at least 8 adults would indicate the Treasury should continue making pennies?

ANSWER:

Solution :

Step 1 of 3:

Let x denotes the treasury should continue making pennies.

Our goal is:

a). We need to find the standard deviation.

b). We need to find the likelihood that exactly 8 adults.

c). We need to find the likelihood that at least 8 adults.

a). Now we have to find the standard deviation.

Then the number of adults has a binomial distribution with parameter n, .

Then the expected number of such adults is

We know that n=15 and 67% = 0.67.

Therefore, the mean is 10.05.

Then the standard deviation formula is

1.8211

Therefore the standard deviation is 1.8211.


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