SOLUTION: 15. Assume the speed of vehicles along the highway has an approximately normal distribution with a mean of 71 mph and a standard deviation of 8 mph.
a. The current speed limit
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-> SOLUTION: 15. Assume the speed of vehicles along the highway has an approximately normal distribution with a mean of 71 mph and a standard deviation of 8 mph.
a. The current speed limit
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Question 1012445: 15. Assume the speed of vehicles along the highway has an approximately normal distribution with a mean of 71 mph and a standard deviation of 8 mph.
a. The current speed limit is 65 mph. What is the proportion of vehicles less than or equal to the speed limit?
b. What proportion of the vehicles would be going less than 50 mph?
c. A new speed limit will be initiated such that approximately 10% of vehicles will be over the speed limit. What is the new speed limit based on this criterion? Answer by stanbon(75887) (Show Source):
You can put this solution on YOUR website! Assume the speed of vehicles along the highway has an approximately normal distribution with a mean of 71 mph and a standard deviation of 8 mph.
a. The current speed limit is 65 mph. What is the proportion of vehicles less than or equal to the speed limit?
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z(65) = (65-71)/8 = -6/8 = = -3/4
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P(x <= 65) = P(z <= -3/4) = normalcdf(-100,-3/4) = 0.2266
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b. What proportion of the vehicles would be going less than 50 mph?
z(50) = (50-71)/8 = -2.625
P(x < 50) = P(z < -2.625) = normalcdf(-100,-2.625) = 0.0043
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c. A new speed limit will be initiated such that approximately 10% of vehicles will be over the speed limit. What is the new speed limit based on this criterion?
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Find the z-value with a left tail of 90%::
invNorm(0.90) = 1.2816
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Find the corresponding speed limit::
x = 1.2816*8 + 71 = 81.25
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Cheers,
Stan H.
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