SOLUTION: A manufacturer knows that their items have a normally distributed lifespan, with a mean of 8.5 years, and standard deviation of 1.2 years.
If you randomly purchase 16 items, wh
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If you randomly purchase 16 items, wh
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Question 1143157: A manufacturer knows that their items have a normally distributed lifespan, with a mean of 8.5 years, and standard deviation of 1.2 years.
If you randomly purchase 16 items, what is the probability that their mean life will be longer than 8 years? Answer by rothauserc(4718) (Show Source):
You can put this solution on YOUR website! The probability(P) that their mean life will be longer than 8 years = 1 - P(X < 8)
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Since the population standard deviation is known, we can use the normal distribution for the sample with the standard error
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standard error(SE) = population standard deviation/square root of sample size
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SE = 1.2/square root(16) = 1.2/4 = 0.3
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z-score(8) = (8 - 8.5)/0.3 = −1.6667 is approximately -1.67
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P associated with z-score of −1.67 is 0.0475 (use z-score tables)
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P(X > 8) = 1 - P(X < 8) = 1 - 0.0475 = 0.9525
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