There are 3600 apples in a shipment. The weight of the apples in this shipment is normally distributed. It is found that it a mean weight of 14 ounces with a standard deviation of 2.5 ounces.

1. How many of apples have weights between 13 ounces and 15 ounces?

2. What is the probability that a randomly selected mango weighs less than 12.5 ounces? Required probability,

3. A quality inspector randomly selected 100 apples from the shipment.

a. What is the probability that the 100 randomly selected apples have a mean weight less than 12.5 ounces?

b. Do you come up with the same result in Question 16? Why or why not?

4. A pharmaceutical company has developed a screening test for a rare disease that afflicted 2% of the population. Unfortunately, the reliability of this test is only 80%, which means that 20% of the tested will get a false positive. If a subject is tested positive based on this test, what is the probability that he has the disease?