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Fundamentals of Statistics | 4th Edition | ISBN: 9780321838704 | Authors: Michael Sullivan,III
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Credit Cards According to creditcard.com, 29% of adults do

Chapter 5, Problem 18AYU

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QUESTION:

Credit Cards According to creditcard.com, \(29 \%\) of adults do not own a credit card.

(a) Suppose a random sample of 500 adults is asked,"Do you own a credit card?" Describe the sampling distribution of \(\hat{p}\), the proportion of adults who own a credit card.

(b) What is the probability that in a random sample of 500 adults more than \(30 \%\) do not own a credit card?

(c) What is the probability that in a random sample of 500 adults between \(25 \%\) and \(30 \%\) do not own a credit card?

(d) Would it be unusual for a random sample of 500 adults to result in 125 or fewer who do not own a credit card? Why?

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QUESTION:

Credit Cards According to creditcard.com, \(29 \%\) of adults do not own a credit card.

(a) Suppose a random sample of 500 adults is asked,"Do you own a credit card?" Describe the sampling distribution of \(\hat{p}\), the proportion of adults who own a credit card.

(b) What is the probability that in a random sample of 500 adults more than \(30 \%\) do not own a credit card?

(c) What is the probability that in a random sample of 500 adults between \(25 \%\) and \(30 \%\) do not own a credit card?

(d) Would it be unusual for a random sample of 500 adults to result in 125 or fewer who do not own a credit card? Why?

ANSWER:

Step 1 of 4

(a) The sampling distribution of  is approximately normal with = 29/100 = 0.29.

Then

 =

 =  

 =

 = 0.020

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