SOLUTION: The average speed of winds in a certain city equals 11 mph. Assume that wind speeds are approximately normally distributed with a standard deviation of 3.5 mph.
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Question 1109719: The average speed of winds in a certain city equals 11 mph. Assume that wind speeds are approximately normally distributed with a standard deviation of 3.5 mph.
(a) Find the probability that the wind speed on any one reading will exceed 13.5 mph.
(b) Find the probability that the mean of a random sample of twelve readings will exceed 13.5 mph. Answer by stanbon(75887) (Show Source):
You can put this solution on YOUR website! The average speed of winds in a certain city equals 11 mph. Assume that wind speeds are approximately normally distributed with a standard deviation of 3.5 mph.
(a) Find the probability that the wind speed on any one reading will exceed 13.5 mph.
z(13.5) = (13.5-11)/3.5 = 2.5/3.5 = 0.7143
P(x > 13.5) = P(z > 0.7143) = normalcdf(0.7143,100) = 0.2375
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(b) Find the probability that the mean of a random sample of twelve readings will exceed 13.5 mph.
z(13.5) = (13.5-11)/[3.5/sqrt(12)] = 2.4744
P(x-bar > 13.5) = P(z > 2.4744) = normalcdf(2.4744,100) = 0.0067
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Cheers,
Stan H.
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