2. A prototype automotive tire has a design life of 38,500 miles deviation of 2,500 miles. The manufacturer tests 60 such tires. that the actual population mean is 38,500 miles and the actual standard deviation is 2 500 miles Assume that the distribution

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2. A prototype automotive tire has a design life of 38,500 miles with a standard
deviation of 2,500 miles. The manufacturer tests 60 such tires. On the assumption
that the actual population mean is 38,500 miles and the actual population
standard deviation is 2,500 miles. Assume that the distribution of lifetimes of such
tires is normal.
(a) Let X = number of miles on a single tire. Find the probability that the sample
mean will be less than 38,000 miles. (Use 4 decimals)
(b) Use a software tool to graph the probability from part (b) (The graph should
show the appropriate area from part (b))
(c) Is the result from part (b) good or bad financially for the manufacturer?
Explain in detail.
ions: On
耳|
Transcribed Image Text:2. A prototype automotive tire has a design life of 38,500 miles with a standard deviation of 2,500 miles. The manufacturer tests 60 such tires. On the assumption that the actual population mean is 38,500 miles and the actual population standard deviation is 2,500 miles. Assume that the distribution of lifetimes of such tires is normal. (a) Let X = number of miles on a single tire. Find the probability that the sample mean will be less than 38,000 miles. (Use 4 decimals) (b) Use a software tool to graph the probability from part (b) (The graph should show the appropriate area from part (b)) (c) Is the result from part (b) good or bad financially for the manufacturer? Explain in detail. ions: On 耳|
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