1. Assume that the waiting time x for an elevator is uniformly distributed between zero and six minutes.

a. Write the formula for the probability curve of x.

b. Graph the probability curve of x.

c. Find P(2 x 4).

d. Find P(3 x 6).

e. Find P({0 x 2} or {5 x 6}).

2. Refer to Exercise 6.8.

a. Calculate the mean, mx, the variance, s2 , and the standard deviation, s .

b. Find the probability that the waiting time of a randomly selected patron will be within one standard deviation of the mean.

3. Consider the figure given in the margin. Find the value k that makes the function f (x) a valid continuous probability distribution.

4. Suppose that an airline quotes a flight time of 2 hours, 10 minutes between two cities. Further- more, suppose that historical flight records indicate that the actual flight time between the two cities, x, is uniformly distributed between 2 hours and 2 hours, 20 minutes. Letting the time unit be one minute,

a. Write the formula for the probability curve of x.

b. Graph the probability curve of x.

c. Find P(125 x 135).

d. Find the probability that a randomly selected flight between the two cities will be at least five minutes late.

Text Book: Business Statics in Practice By BOWERMAN.