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17. A psychic network received telephone calls last year from over 1.5 million people. To test the credibility of the psychic network, an experiment was conducted and, 5 different cards were shuffled, and 1 is chosen at random. The psychic will then try to identify which card was drawn without seeing it. Assume that the experiment was repeated 45 times and that the results of any 2 experiments are independent of one another. If we assume that the psychic is fake, find the probability that they guess at least 3 correctly.
Solution: If the psychic is a fake, then he’ll pick randomly, and therefore has 20% chances to be right. Let
be the number of correct answers. Thenhas a binomial distribution with parameters
and
. Then
18. The on-line access computer service industry is growing at an extraordinary rate. Current estimates suggest that only 45% of the home-based computers have access to on-line services. This number is expected to grow quickly over the next five years. Suppose 25 people with home-based computers were randomly and independently sampled. Find the probability that more than five but fewer than 8 currently have access to on-line services.
Solution: Letbe the number of people who have access to on-line services, out of the sample of 25 people. Thenhas a binomial distribution with parameter
and
. Hence, the probability that more than five but fewer than 8 currently have access to on-line services is equal to
19. Sales of a new line of athletic footwear are crucial to the success of a newly formed company. The company wishes to estimate the avg. weekly sales of the new footwear to within $150 with 98% reliability. The initial sales indicate the standard deviation of the weekly sales figures are approx. $1525. How many weeks of data must be sampled for the company to get the information it desires?
Solution: The 98% Margin of error is equal to
We need to estimate the avg. weekly sales of the new footwear to within $150 with 98%, which means
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