A normal population has a mean of $75 and standard deviation of $5. You select random samples of 40. a. Apply the central limit theorem to describe the sampling distribution of the sample mean with n = 40. What condition is necessary to apply the central limit theorem? b. What is the standard error of the sampling distribution of sample means? (Round your answer to 2 decimal places.) c. What is the probability that a sample mean is less than $74? (Round z-value to 2 decimal places and final answer to 4 decimal places.) d. What is the probability that a sample mean is between $74 and $76? (Round z-value to 2 decimal places and final answer to 4 decimal places.) e. What is the probability that a sample mean is between $76 and $77? (Round z-value to 2 decimal places and final answer to 4 decimal places.) f. What is the probability that the sampling error ( xx ) would be $1.50 or less? (Round z-value to 2 decimal places and final answer to 4 decimal places.)