1. The random variable x is known to be uniformly distributed between 1.0 and 1.5.

a. Show the graph of the probability density function.

b. Compute P(x = 1.25).

c. Compute P(1.0 ? x ? 1.25).

d. Compute P(1.20

2. The random variable x is known to be uniformly distributed between 10 and 20.

a. Show the graph of the probability density function.

b. Compute P(x

c. Compute P(12 ? x ? 18).

d. Compute E(x).

e. Compute Var(x).

3. Delta Airlines quotes a flight time of 2 hours, 5 minutes for its flights from Cincinnati to Tampa. Suppose we believe that actual flight times are uniformly distributed between 2 hours and 2 hours, 20 minutes.

a. Show the graph of the probability density function for flight time.

b. What is the probability that the flight will be no more than 5 minutes late?

c. What is the probability that the flight will be more than 10 minutes late?

d. What is the expected flight time?

5. In October 2012, Apple introduced a much smaller variant of the Apple iPad, known as the iPad Mini. Weighing less than 11 ounces, it is about 50% lighter than the standard iPad. Battery tests for the iPad Mini showed a mean life of 10.25 hours (The Wall Street Journal, October 31, 2012). Assume that battery life of the iPad Mini is uniformly distributed between 8.5 and 12 hours.

a. Give a mathematical expression for the probability density function of battery life.

b. What is the probability that the battery life for an iPad Mini will be 10 hours or less?

c. What is the probability that the battery life for an iPad Mini will be at least 11 hours?

d. What is the probability that the battery life for an iPad Mini will be between 9.5 and 11.5 hours?

e. In a shipment of 100 iPad Minis, how many should have a battery life of at least 9 hours?

8. Using Figure 6.4 as a guide, sketch a normal curve for a random variable x that has a mean of ? = 100 and a standard deviation of ? = 10. Label the horizontal axis with values of 70, 80, 90, 100, 110, 120, and 130.

FIGURE 6.4 AREAS UNDER THE CURVE FOR ANY NORMAL DISTRIBUTION

99.7% 95.4% 68.36- 4-30 4+ 30 H-20 #+2099.7% 95.4% 68.36- 4-30 4+ 30 H-20 #+20