Suppose the parent population has an exponential distribution with a mean of 15 and standard deviation of 12. Use the Central Limit Theorem to describe the distribution of when drawing samples of size 30.

The sampling distribution of the sample mean of size 30 will be approximately normal with mean 15 and standard deviation 2.19.

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 the population, we have that:

Mean = 15

Standard deviaiton = 12

Sample of 30

By the Central Limit Theorem

Mean 15

Standard deviation

Approximately normal

The sampling distribution of the sample mean of size 30 will be approximately normal with mean 15 and standard deviation 2.19.

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step-by-step explanation:

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step-by-step explanation: