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Test scores are normally distributed with a mean of 76 and a standard deviation of 10. a. In a group of 230 tests, how many students score above 96? b. In a group of 230 tests, how many students score below 66? c. In a group of 230 tests, how many students score within one standard deviation of the mean? The number of nails of a given length is normally distributed with a mean length of 5.00 in. and a standard deviation of 0.03 in. a. Find the number of nails in a bag of 120 that are less than 4.94 in. long. b. Find the number of nails in a bag of 120 that are between 4.97 and 5.03 in. long. c. Find the number of nails in a bag of 120 that are over 5.03 in. long. 3 The actual weights of bags of pet food are normally distributed. The mean of the weights is 50.0 lb, with a standard deviation of 0.2 lb. Use the graph for a - c. a. About what percent of bags of pet food weigh less Weight of bags than 49.8 lb? 20 b. In a group of 250 bags, how many would you expect to weigh more than 50.4 lb? Percent of bags 50.5 c. In a group of 50 bags, how many would you expect to Weight (In pounds) be within 1.5 standard deviations of the mean? 4 Battery lifetime is normally distributed for large samples. The mean lifetime is 500 days and the standard deviation is 61 days. Approximately what percent of batteries have lifetimes longer than 561 days? 5 A test was given to 120 students, and the scores approximated a normal distribution. If the mean score was 72 with a standard deviation of 7, approximately what percent of the scores were 65 or higher? The average life of a refrigerator is 14 years with a standard deviation of 2.5 years. A company has a guarantee program that will replace the product if it breaks. How many years (round to nearest tenth) should they guarantee the product if they don't want to replace more than 5% of the refrigerators