# Question

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?

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?

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