1. Suppose that an airline quotes a flight time of 2 hours, 10 minutes between two cities. Furthermore, 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. Let 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.

2. Suppose that the 33rd percentile of a normal distribution is equal to 656 and that the 97.5th percentile of this this normal distribution is 896. Find the mean and standard deviation of the normal distribution.

3. A fair die is rolled n = 54 times and four sixes are observed.

1. Describe the sampling distribution of sample proportion by stating its mean, variance, and shape. Did you have to make any assumption?
2. Based on the sampling information, is there statistical evidence to suggest that the die is not fair, that in fact p is less than 1/6 for the sixes?