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Answer:
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