Apple claims that with a fully charged battery, users of its iPhone 11 can stream video up to 10 hours. The minimum battery life for streaming video is 7.5 hours. Assume that for a randomly selected iPhone 11, battery life is uniformly distributed between 7.5 and 10 hours. The density function of this uniform probability distribution is given in the figure below.

For values of battery life between 7.5 and 10 hours, the density is 0.4. For all other values of battery life, the density is 0.

1.In the figure above, indicate the probability that a randomly selected iPhone 11 has a battery life between 9 and 10 hours. What is the value of this probability?

2.Calculate the probabilities that

a.the battery life is between 7.5 and 8 hours; and

b.the battery life is less than 8 hours.

Are these two probabilities different? Explain why or why not.

3.Suppose that you randomly picked 100 iPhones and calculated the average battery life for these phones. Provide your best guess of the value of the average.