Geometric Distribution · Example 3
The lifetime risk of developing cancer is about one in 67 (1.5%). Let X = the number of people you ask before one says they have cancer. The random variable X in this case includes only the number of trials that were failures and does not count the trial that was a success in finding a person who had the disease. The appropriate formula for this random variable is the second one presented above. Then X is a discrete random variable with a geometric distribution:
(a) What is the probability that you ask 9 people before one says they have cancer? This is asking, what is the probability that you ask 9 people who say no and the tenth person says yes?
(b) What is the probability that you must ask 20 people?
(c) Find the (i) mean and (ii) standard deviation of X.
OpenStax, Introductory Business Statistics 2e · §4.3 Geometric Distribution · Example 3
No hints for this one.
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