A small company in Yoknapatawpha manufactures smoke detectors. It is known that the average lifetime of...
A small company in Yoknapatawpha manufactures smoke detectors. It is known that the average lifetime of that company’s smoke detectors is 5 years. If the standard deviation of the lifetime of the smoke detectors is 8 months, find the probability that a random sample of 30 smoke detectors will have a mean lifetime between 58 and 63.
Homework Answers
mean = 5 * 12 = 60 months
sd = 8
n = 30
Z = (X - mean) / (sd / sqrt(n))
P(58 < X < 63) = P((58 - 60)/(8/sqrt(30)) < Z < (63 - 60)/(8/sqrt(30)))
= P(-1.37 < Z < 2.05)
= P(Z < 2.05) - P(Z < -1.37)
= 0.9798 - 0.0853
= 0.8945
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