According to a survey in a country, 29% of adults do not have any credit cards.

Question

According to a survey in a country, 29% of adults do not have any credit cards. Suppose a simple random sample of 400 adults is obtained. Answer questions (a) Through (c)

(a) Describe the sampling distribution of ModifyingAbove p with caretp, the sample proportion of adults who do not have a credit card. Choose the phrase that best describes the shape of the sampling distribution of ModifyingAbove p with caretp below. A. Approximately normal because n less than or equals 0.05 Upper Nn0.05N and np left parenthesis 1 minus p right parenthesis greater than or equals 10.np(1p)10.

B. Not normal because n less than or equals 0.05 Upper Nn0.05N and np left parenthesis 1 minus p right parenthesis greater than or equals 10.np(1p)10.

C. Approximately normal because n less than or equals 0.05 Upper Nn0.05N and np left parenthesis 1 minus p right parenthesis less than 10.np(1p)<10.

D. Not normal because n less than or equals 0.05 Upper Nn0.05N and np left parenthesis 1 minus p right parenthesis less than 10.np(1p)<10.

Determine the mean of the sampling distribution of ModifyingAbove p with caretp. mu Subscript ModifyingAbove p with caret Baseline equalsp=nothing (Round to two decimal places as needed.)

Determine the standard deviation of the sampling distribution of ModifyingAbove p with caretp. sigma Subscript ModifyingAbove p with caretpequals=nothing (Round to three decimal places as needed.)

(b) In a random sample of 400 adults, what is the probability that less than 26% have no credit cards? The probability is nothing. (Round to four decimal places as needed.)

(c) Would it be unusual if a random sample of 400 adults results in 132 or more having no credit cards?

A. The result is notis not unusual because the probability that ModifyingAbove p with caretp is greater than or equal to this sample proportion is greatergreater than 5%.

B. The result is notis not unusual because the probability that ModifyingAbove p with caretp is greater than or equal to this sample proportion is lessless than 5%.

C. The result isis unusual because the probability that ModifyingAbove p with caretp is greater than or equal to this sample proportion is greatergreater than 5%.

D. The result isis unusual because the probability that ModifyingAbove p with caretp is greater than or equal to this sample proportion is lessless than 5%.

Explanation / Answer

(a) n = 400, p = 0.29

A. Approximately normal because n less than or equals 0.05 Upper Nn0.05N and np left parenthesis 1 minus p right parenthesis greater than or equals 10.np(1p)10.

(b) x = 400 * 0.26 = 104 (103.5), = np = 400 * 0.29 = 116, = (npq) = (400 * 0.29 * 0.71) = 9.08

z = (x - )/ = (103.5 - 116)/9.08 = -1.3767

P(x < 103.5) = P(z < -1.3767) = 0.0843

(c) A. The result is not unusual because the probability that ModifyingAbove p with caretp is greater than or equal to this sample proportion is greater than 5%.

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