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Answer:
The sampling distribution of the sample proportion of adults who have credit card debts of more than $2000 will be normally distributed with mean = 0.38 and standard deviation of 0.034.
Step-by-step explanation:
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, the sampling distribution will be normally distributed with mean and standard deviation
In this problem, we have that:
So
The sampling distribution of the sample proportion of adults who have credit card debts of more than $2000 will be normally distributed with mean = 0.38 and standard deviation of 0.034.