Question

According to a study conducted in one city, 38% of adults in the city have credit card debts of more than $2000. A simple random sample of n = 250 adults is obtained from the city. Describe the sampling distribution of p, the sample proportion of adults who have credit card debts of more than $2000. Round to three decimal places when necessary. O A. Exactly normal; Hp = 0.38, Op = 0.031 O B. Binomial; Hp = 95, p = 7.675 O C. Approximately normal; Hp = 0.38, Op = 0.031 O D. Approximately normal; Hp = 0.38, op = 0.001

Answer 1

The sampling distribution of p, the sample proportion of adults who have credit card debts of more than $2000, can be approximated as normal when certain conditions are met. In this case, the conditions are satisfied, indicating that the sampling distribution of p is approximately normal.

Step-by-step explanation:

The sampling distribution of p, the sample proportion of adults who have credit card debts of more than $2000, can be approximated as normal when certain conditions are met. In this case, we have a simple random sample of n = 250 adults from the city, where 38% of adults have credit card debts of more than $2000. To determine if the sampling distribution of p is approximately normal, we need to check if both np and n(1-p) are greater than or equal to 5. In this case, np = 250(0.38) = 95 and n(1-p) = 250(0.62) = 155, both of which are greater than 5. Therefore, we can conclude that the sampling distribution of p is approximately normal.