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.
- Describe the sampling distribution of sample proportion by stating its mean, variance, and shape. Did you have to make any assumption?
- 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?