SOLUTION: 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 dev

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Question 836010: 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 4mph.
a. find the mean of all speeds if 3% of the automobiles travel faster than 72 mph.
b. using the mean you found in a, find the probability that a car is traveling between 70mph and 75mph. (considering normal probability distribution)
c. using the mean in a, find the 25th percentile for the variable "speed"
Answer by new_user(6) About Me  (Show Source):
You can put this solution on YOUR website!
a) Let the mean be represented by M.
Critical Z value: Z* = (X - M)/S
S = Population standard deviation = 4 mph
X = Test statistic = 72 mph
Given p(X>72) = 0.03 i.e. p(X<=72) = 1 - 0.03 = 0.97

Using standard normal distribution table
So for p = 0.97, Z* = 1.88

1.88 = (72 - M)/4
M = 64.48

So mean speed is 64.48 mph.

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