SOLUTION: An aircraft strobe light is designed so that the times between flashes are normally distributed with a mean of 3 seconds and a standard deviation of 0.96 seconds. Find the probabil

Question 1069076: An aircraft strobe light is designed so that the times between flashes are normally distributed with a mean of 3 seconds and a standard deviation of 0.96 seconds. Find the probability that the mean for 30 randomly selected times is between 2.70 and 3.14 seconds. Express the probability in the nearest four decimal places.
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Answer by rothauserc(4718) (Show Source): You can put this solution on YOUR website!
Probability(P) ( 2.70 < X < 3.14 ) = P ( X < 3.14 ) - P ( X < 2.70 )
:
Calculate z-score for X < 2.70
z-score = (2.70 - 3 ) / ((0.96)/(square root(30)) = −1.7116
use table of z-values to find the associated P
P ( X < 2.70) = 0.0436
:
Calculate z-score for X < 3.14
z-score = (3.14 - 3) / ((0.96)/(square root(30)) = 0.7988
P ( X < 3.14 ) = 0.7881
:
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Probability(P) ( 2.70 < X < 3.14 ) = 0.7881 - 0.0436 = 0.7445
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