Probability, confidence interval, analysis sample questions

The area under the normal curve between z=1 and z=2 is ________________ the area under the normal curve between z=2 and z=3.
A. Greater than
B. Less than
C. Equal to
D. A, B or C above dependent on the value of the mean
E. A, B or C above dependent on the value of the standard deviation

Essay Type Questions Please show work and formula's Answers in Microsoft Word format (Copy Excel to Word)

In a study conducted for the State Department of Education, 30% of the teachers who left teaching did so because they were laid off. Assume that we randomly select 12 teachers who have recently left their profession. Find the probability that at least 7 of them were laid off.

The weight of a product is normally distributed with a standard deviation of 1.5 ounces. What should the average weight be if the production manager wants no more than 5% of the products to weigh more than 15 ounces?

A PGA (Professional Golf Association) tournament organizer is attempting to determine whether hole (pin) placement has a significant impact on the average number of strokes for the 13th hole on a given golf course. Historically, the pin has been placed in the front right corner of the green and the historical mean number of strokes for the hole has been 4.25, with a standard deviation of 1.4 strokes. On a particular day during the most recent golf tournament, the organizer placed the hole (pin) in the back left corner of the green. 49 golfers played the hole with the new placement on that day. Determine the probability of the sample average number of strokes being greater than 4.35.

The population of lengths of aluminum-coated steel sheets is normally distributed with a mean of 30.05 inches and a standard deviation of 0.32 inches. A sample of 16 metal sheets is randomly selected from a batch. What is the probability that the average length of a sheet is between 29.95 and 30.25 inches long?

The production manager for the XYZ manufacturing company is concerned that the customer orders are being shipped late. He asked one of his planners to check the timeliness of shipments for the orders. The planner randomly selected 900 orders and found that 180 orders were shipped late. Construct the 95% confidence interval for the proportion of orders shipped late.