Question 1012445
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.