Many homeowners rely on handymen to perform small jobs, such as repairs or maintenance, around their residence. According to HomeAdvisor Inc., the average cost for a handyman project is $ 460. Assume the population standard deviation is $ 95. A random sample of 30 handyman projects was selected.

a. What is the probability that the sample mean will be less than $ 475?

b. What is the probability that the sample mean will be between $ 450 and $ 465?

c. Identify the symmetrical interval that includes 95% of the sample means if the true population mean is $ 460 per project.

d. Suppose the sample mean was $ 411. Does this result support the findings of HomeAdvisor Inc.?