1. Determine the value of z* such that
a. -z* and z* separate the middle 95% of all z values from the most extreme 5%
b. -z* and z* separate the middle 90% of all z values from the most extreme 10%
c. -z* and z* separate the middle 98% of all z values from the most extreme 2%
d. -z* and z* separate the middle 92% of all z values from the most extreme 8%
2. Suppose that 5% of cereal boxes contain a prize and the other 95% contain the message, "Sorry, try again." Consider the random variable x, where x = number of boxes purchased until a prize is found.
a. What is the probability that at most two boxes must be purchased?
b. What is the probability that exactly four boxes must be purchased?
c. What is the probability that more than four boxes must be purchased?