1) The weights of the fish in a certain lake are normally distributed with a mean of 20 lb and a standard deviation of 6. If 9 fish are randomly selected, what is the likelihood that the mean weight will be between 17.6 and 21.6 lb?
2) A bank’s loan officer rates applicants for credit. The ratings are normally distributed with a mean of 200 and a standard deviation of 50. If an applicant is randomly selected, find the probability of a rating that is between 225 and 275.
3) The lifetimes of projector bulbs of a particular type are normally distributed with a mean of 470 hours and a standard deviation of 15 hours. What percentage of the bulbs has lifetimes that lie within 2 standard deviations of the mean on either side? Apply the 68-95-99.7 Rule this question.
4) The annual precipitation for one city is normally distributed with a mean of 28 inches and a standard deviation of 3.4 inches. Fill in the blanks. In 95% of the years, the precipitation in this city is between andinches. Apply the 68-95-99.7 rule to this question.
5) The systolic blood pressures of the patients at a hospital are normally distributed with a mean of 136 mm Hg and a standard deviation of 12 mm Hg. Find the two blood pressures having these properties: the mean is midway between them and 76.98% of all blood pressures are between them.
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