The average number of units that the factory workers at Shilo Company assemble per week is µ = 45 with a standard deviation of s = 12. Assume that the distribution of units assembled is normal. If a sample n = 25 were drawn from all of the workers,
a. What range of units manufactured by this sample would contain the sample mean 90% of the time? (Hint: Find the middle 90% of the distribution of sample means.)
b. What is the probability that the sample mean will be between 40 and 50 units?
c. Is it reasonable for this sample to produce an average of 48 units per week, or is this mean very different from what would be normally expected?
d. How likely is it that this sample will produce more than an average of 55 units?