Sampling Distributions and The Central Limit Theorem

As the size of a sample increases, the mean of the sampling distribution increases.

• True

• False

A sampling distribution is normal only if the population is normal.

• True

• False

As the size of a sample increases, the standard deviation of the sampling distribution decreases.

• True

• False

A bank auditor claims that credit card balances are normally distribution with a mean of $3,500 and a standard deviation of $1,250. A random sample of size 50 is taken. What are the mean and standard deviation of the sampling distribution?

A bank auditor claims credit card balances are normally distributed, with a mean of $3,500 and a standard deviation of $1,250. A random sample of 25 individuals is taken. What is the probability that the mean of the credit cards is less than $3180?

• 0.3085

• 0.4801

• 0.1003

• 0.1151

A bank auditor claims credit card balances are normally distributed, with a mean of $3,500 and a standard deviation of $1,250. A random sample of 25 individuals is taken. What is the probability that the mean of the credit cards is greater than $4,100?

• 0.0082

• 0.9918

• 0.5398

• 0.4602

A bank auditor claims credit card balances are normally distributed, with a mean of $3,500 and a standard deviation of $1,250. A random sample of 25 individuals is taken. What is the probability that the mean of the credit cards is between $3200 and 3,425?

• 0.0159

• 0.2670

• 0.5028

• 0.4972