Question

8 Question Help 8.2.18 According to a survey in a country, 39% of adults do not own a credit card. Suppose a simple random sample of 400 adults is obtained. Complete parts (a) through (d) below. Click here to view the standard normal distribution table (page 1). Click here to view the standard normal distribution table (page 2) (a) Describe the sampling distribution of p, 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 p below. A. Not normal because ns 0.05N and np(1-p) > 10 B. Approximately normal because n s 0.05N and np(1-P)< 10 C. Approximately normal because ns0.05N and np(1-P) 2 10 D. Not normal because ns 0.05N and np(1-p) < 10 Determine the mean of the sampling distribution of p. HA=(Round to two decimal places as needed.)

Answer 1

Answer

Option C is correct.

Explanation

The condition for the distribution to be approximately normal is for p to be fairly balanced between 0 and 1, and np > 0 or np(1 - p) > 0.

n = 400

p = 39% = 0.39

np = (400) (0.39) = 156 > 10

np(1 - p) = (400) (0.39) (1 - 0.39) = (156) (0.61) = 95.16 > 10

Hence, we can conclude that this distribution is approximately normal.

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