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M ⁼⁼ 125 mg/dl and er = 10 mg/dl. What is the level L such that there is probability only 0.05 that the mean glucose level of 4 test results falls above L for Sheilas glucose level distribution?

5.38 A company that owns and services a fleet of cars for its sales force has found that the service lifetime of disc brake pads varies from car to car according to a normai distribution with mean /jl Hf 55, 000 miles and standard deviation a jfe? 4500 miles. The company installs a new brand of brake pads on 8 cars.

(a)    If the new brand has the same lifetime distribution as the previous type, what is the distribution of the sample mean lifetime for the 8 cars?

(b)    The average life of the pads on these 8 cars tums out to be x — 51,800 miles. What is the probability that the sample mean lifetime is 51,800 miles or less if the lifetime distribution is unchanged? The company takes this probability as eridence that the average lifetime of the new brand of pads is less than 55,000 miles.

5.39 The number of flaws per sąuare yard in a type of carpet materiał varies with mean 1.6 flaws per sąuare yard and standard deriation 1.2 flaws per sąuare yard. This population distribution cannot be normai, because a count takes only whole-number values. An inspector studies 200 sąuare yards of the materiał, records the number of flaws found in each sąuare

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