A True-False test has 20 questions with each having 2 possible answers with one correct. Assume a student randomly guesses the answer to every question.
a. What is the probability of getting exactly 9 correct answers?
b. What is the probability of getting less than 6 correct answers?
3a. The diameters of a wooden dowel produced by a new machine are normally distributed with a mean of 0.55 inches and a standard deviation of 0.01 inches. What percent of the dowels will have a diameter less than 0.57?
3b. The a loan officer rates applicants for credit. Ratings are normally distributed. The mean is 240 and the standard deviation is 50. Find the probability that an applicant will have a rating greater than 300.
4. Answer the questions about the specified normal distribution.
a. The lifetime of ZZZ batteries are normally distributed with a mean of 265 hours and a standard deviation of 10 hours. Find the number of hours that represent the the 40th percentile.
b. Scores on an English placement test are normally distributed with a mean of 36 and standard deviation of 6.5. Find the score that marks the top 5%.
5. Find the probabilities.
a. From National Weather Service records, the annual snowfall in the TopKick Mountains has a mean of 92 inches and a standard deviation of 12 inches. If the snowfall from 25 randomly selected years are chosen, what it the probability that the snowfall would be less than 95 inches?
b. The loan officer rates applicants for credit. Ratings are normally distributed. The mean is 240 and the standard deviation is 60. If 36 applicants are randomly chosen, what is the probability that they will have a rating between 230 and 260?
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