EXAM 2 Free Response Section Part 1 A laboratory test for the detection of a certain disease gives a positive result 5 percent of the time for people who do not have the disease. The test gives a negative result 0.2 percent of the time for people who have the disease. Large-scale studies have shown that the disease occurs in about 3 percent of the population. A) What is the probability that a person selected at random would test positive for this disease? Fill in the blanks and calculate the final probability. ⬚ ∗ 0.998 + 97 ∗ ⬚ 100 = B) Use the probability in part A to find the probability that a person selected at random who tests positive for the disease does not have the disease? Show your work. Kentucky Fish and Wildlife recently helped stocked a new lake in a city park with 1,500 fish of various sizes. The distribution of the lengths of these fish is approximately normal. a) Suppose the standard deviation of the sampling distribution of the sample mean for random samples of size 50 is 0.3 inch. If the mean length of the fish is 7.5 inches, draw a diagram of the normal distribution that represents this situation. Be sure to label all parts. b) Use the normal distribution (with a table or calculator) to compute the probability that a random sample of 50 fish will have a mean length less than 7.2 inches. Justify your answer. BONUS: What is the probability that a random sample of 50 fish will have a mean length between 7.2 and 7.5 inches? Justify your answer.
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