Health: Hip Replacement According to the National Institute of Health, approximately one in four people will develop symptomatic hip osteoarthritis in their lifetime. In a group of 4 people, let’s say that success is not developing osteoarthritis.

(a) What is the probability of success, p, in this situation?

(b) Find the probability P r ( ) of r successes ranging from 0 to 4.

(c) Make a histogram of the probability distribution in part (b).

(d) What is the expected number of people out of 4 that do not develop osteoarthritis? What is the standard deviation?

(e) Quota Problem How large a group of people should we have to be about 98% sure that three or more of the people do not develop osteoarthritis in their lifetimes?

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