Question

Annual automobile insurance cost for Americans is uniformly distributed from $200 to $1,182. Suppose 15 Americans are randomly and independently sampled. What is the probability that 10 of them pay between $410 and $825 for auto insurance (round your answer to four decimal places)?

Lifetime of a randomly selected Bright Star lightbulb is exponentially distributed with a mean of 400 hours. Suppose Joe has a Bright Star lightbulb that has lasted 600 hours and is still working, and Becky has a Bright Star lightbulb that is brand new. Joe makes the following statement to Becky: “Since my lightbulb has already lasted 600 hours, the probability that my lightbulb will last at least 200 more hours (i.e. 800 hours) is smaller than the probability that your brand new lightbulb will last at least 200 hours”. Is Joe’s statement correct? Explain your answer.

Suppose that the lifetime of Outlast batteries is normally distributed with a mean of 240 hours. The company is trying to decrease the standard deviation of the lifetime of the batteries so as to improve the reliability of their product. Suppose the goal is to make all of the batteries such that only 20% of the batteries last less than 219 hours. What should the standard deviation be in order to reach this goal? For this extra credit you must show all of your work and round your answer to four decimal places. Hint: Thinking in terms of a z-score is helpful.

Answer 1