Question

1. An apple juice producer buys all his apples from a conglomerate of apple growers in one northwest state. The amount of juice squeezed from each of these apples is approximately normally distributed with a mean of 2.15 ounces and a standard deviation of 0.15 ounce.

1. What is the probability that a randomly selected apple will contain less than 1.90 ounces?
2. What is the probability that a randomly selected apple will contain between 1.90 and 2.40 ounces?
3. What is the probability that a randomly selected apple will contain more than 2.40 ounces?
4. 77% of the apples will contain at least how many ounces of juice?

2. While conducting experiments, a marine biologist selects water depths from a uniformly distributed collection that vary between 2.00 m and 7.00 m.

1. What is the probability that a randomly selected depth is less than 3.50 m?
2. What is the probability that a randomly selected depth is between 2.15 m and 5.50 m?
3. What is the expected value of the water depth?
4. What is the standard deviation of the water depth?

3. An important part of the customer service responsibilities of a cable company relates to the speed with which trouble in service can be repaired. Historically, the data show that the likelihood is 0.85 that troubles in a residential service can be repaired on the same day. Use the binomial formula to calculate.

1. For the first five troubles reported on a given day, what is the probability that: All five will be repaired on the same day?
2. For the first five troubles reported on a given day, what is the probability that: Fewer than two troubles will be repaired on the same day?
3. For the first five troubles reported on a given day, what is the probability that: At least 3 troubles will be repaired on the same day.
4. Find the mean number of troubles repaired on the same day?

Answer 1