Question 638305
A radar unit is used to measure the speed of automobile on an expressway during rush-hour traffic. The speeds of individual automobiles are normally distributed with a standard deviation of 4 mph.
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Sketch a normal curve with u = ? and sigma = 4
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a. Find the mean of all speeds if 3% of the automobiles travel faster than 72 mph. Round the mean to the nearest tenth.
Mark a point on the horizontal axis with a right-tail of 3%.
Mark the point as x = 72.
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Find the z-value that has a right tail of 3%:
invNorm(0.97) = 1.8808
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Now find "u":
x = z*s + u
72 = 1.8808*4 + u
u = 64.4768 = 64.5 mph when rounded
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b. Using the mean you found in part a, find the probability that a car is traveling between 70 mph and 75 mph. Interpret the meaning of this answer.
z(70) = (70-64.5)/4 = 1.375
z(75) = (75-64.5)/4 = 2.625
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P(70<= x <=75) = P(1.375<= z <=2.625) = 0.08
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c. Using the mean you found in part a, find the 25th percentile for the variable "speed".
Find the z-value with a left-tail of 25%
invNorm(0.25) = -0.6745
Find the corresponding x value:
x = zs+u = -0.6745*4+64.5 = 61.8 mph
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Cheers,
Stan H.
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