Question

According to a survey in a​ country, 39​% of adults do not own a credit card. Suppose a simple random sample of 200 adults is obtained. Complete parts​ (a) through​ (d) below. Click here to view the standard normal distribution table (page 1). LOADING... Click here to view the standard normal distribution table (page 2). LOADING... ​(a) Describe the sampling distribution of ModifyingAbove p with caret​, the sample proportion of adults who do not own a credit card. Choose the phrase that best describes the shape of the sampling distribution of ModifyingAbove p with caret below. A. Not normal because n less than or equals 0.05 Upper N and np left parenthesis 1 minus p right parenthesis greater than or equals 10 B. Approximately normal because n less than or equals 0.05 Upper N and np left parenthesis 1 minus p right parenthesis less than 10 C. Approximately normal because n less than or equals 0.05 Upper N and np left parenthesis 1 minus p right parenthesis greater than or equals 10 D. Not normal because n less than or equals 0.05 Upper N and np left parenthesis 1 minus p right parenthesis less than 10 Determine the mean of the sampling distribution of ModifyingAbove p with caret. mu Subscript ModifyingAbove p with caret Baseline equals nothing ​(Round to two decimal places as​ needed.) Determine the standard deviation of the sampling distribution of ModifyingAbove p with caret. sigma Subscript ModifyingAbove p with caretequals nothing ​(Round to three decimal places as​ needed.) ​(b) What is the probability that in a random sample of 200 ​adults, more than 41​% do not own a credit​ card? The probability is nothing. ​(Round to four decimal places as​ needed.) Interpret this probability. If 100 different random samples of 200 adults were​ obtained, one would expect nothing to result in more than 41​% not owning a credit card. ​(Round to the nearest integer as​ needed.) ​(c) What is the probability that in a random sample of 200 ​adults, between 36​% and 41​% do not own a credit​ card? The probability is nothing. ​(Round to four decimal places as​ needed.) Interpret this probability. If 100 different random samples of 200 adults were​ obtained, one would expect nothing to result in between 36​% and 41​% not owning a credit card. ​(Round to the nearest integer as​ needed.) ​(d) Would it be unusual for a random sample of 200 adults to result in 72 or fewer who do not own a credit​ card? Why? Select the correct choice below and fill in the answer box to complete your choice. ​(Round to four decimal places as​ needed.) A. The result is not unusual because the probability that ModifyingAbove p with caret is less than or equal to the sample proportion is nothing​, which is greater than​ 5%. B. The result is unusual because the probability that ModifyingAbove p with caret is less than or equal to the sample proportion is nothing​, which is greater than​ 5%. C. The result is not unusual because the probability that ModifyingAbove p with caret is less than or equal to the sample proportion is nothing​, which is less than​ 5%. D. The result is unusual because the probability that ModifyingAbove p with caret is less than or equal to the sample proportion is nothing​, which is less than​ 5%.

Answer 1

(A)

C. Approximately normal because n < 0.05N and np(1-p)>= 10

Here we have

n=200, p=0.39

The sampling distribution of sample proportion will be approximately normal distribtuion with mean

and standard deviation

(B)

The z-score for is

The probability that in a random sample of 200 adults, more than 41% do not own a credit card is

P(z > 0.58) = 0.2810

If 100 different random samples of 200 adults were obtained, one would expect = 100 * 0.2810 = 28.10 or 28 to result in more than 28% not owning a credit card.

(c)

The z-score for is

The z-score for is

The probability that in a random sample of 200 adults, between 36% and 41% do not own a credit card is

P(-0.87 < z < 0.58) = 0.5269

If 100 different random samples of 200 adults were obtained, one would expect = 100 * 0.5269= 52.69 or 53 to result in between 36% and 41% not owning a credit card.

(d)

The z-score for is

So,

A. The result is not unusual because the probability that is less than or equal to the sample proportion is 0.1922​, which is greater than​ 5%