The average number of products that the assembly line workers at Style-X Company assemble per day is = 40 with a standard deviation of = 15. Assume that the distribution of units assembled is normal. If a sample n = 25 were drawn from all of the workers:

1. What range of units manufactured by this sample would contain the sample mean 90% of the time? (Hint: First find the middle 90% of the distribution of sample means.) (5 pts)
2. What is the probability that the sample mean will be between 35 and 49 units? (5 pts)
3. Is it reasonable for this sample to produce an average of 44 products per day, or is this mean very different from what would be normally expected? (5 pts)
4. How likely is it that this sample will produce more than an average of 55 products per day? (5pts)