According to a study conducted in one city, 39% of adults in the city have credit card debts of more than $2000. A simple random sample of 100 adults is obtained from the city. Describe the sampling distribution of the sample proportion of adults who have credit card debts of more than $2000.

The sampling distribution of the sample proportion of adults who have credit card debts of more than $2000 is approximately normally distributed with mean and standard deviation

Step-by-step explanation:

Central Limit Theorem

The Central Limit Theorem estabilishes that, for a normally distributed random variable X, with mean and standard deviation , the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean and standard deviation .

For a skewed variable, the Central Limit Theorem can also be applied, as long as n is at least 30.

For a proportion p in a sample of size n, the sampling distribution of the sample proportion will be approximately normal with mean and standard deviation

In this question:

Then

By the Central Limit Theorem:

The sampling distribution of the sample proportion of adults who have credit card debts of more than $2000 is approximately normally distributed with mean and standard deviation

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step-by-step explanation: