1. A new surgical procedure is said to be successful 80% of the time. Suppose the procedure is performed five times and the results are assumed to be independent of one another. What is the probability that a. all procedures are successful? b. exactly four are successful c. less than two are successful
2. An insurance salesman sells policies to 5 men, all of identical age and in good health. if the probability that a man of this particular age will be alive in 30 years is 2/3. Find the probability that in 30 years a. 5 men will be alive b. at least 3 men will be alive; c. only 2 men will be alive d. at least one man will be alive.
3. In a Mathematics examination, the average score was 82 and the standard deviation was 5. All students with scores from 88 to 94 received a grade of B. if the scores are approximately normally distributed and 8 students received a B grade, how many students took the examination?
4. The mean weight of 500 male students at a certain college is 151lbs., and the standard deviation is 15lbs. Assuming that the weights are normally distributed and weights are recorded to the nearest kilogram, find a. how many students weigh less than or equal to 128 lbs.? b. how many students weight more than 185 lbs? c/ How many students weight between 120 and 155lbs.?
5. A used car dealer, has found that the length of time before a major repair is required on the cars it sells is normally distributed with a mean equal to 10 months and a standard deviation equal to 3 months, If the dealer only wants 5% of the cars to fail before the end of the guarantee period, for how many months should the cars be guaranteed?