A taxi company determined that the distance traveled per taxi per year in its entire fleet was normally distributed with a mean of 12 thousand miles and a standard deviation of 4 thousand miles. a) A taxi in the fleet traveled 7 thousand miles in the last year. Calculate the z-score for this taxi.
b) Interpret the z-score from part a.
c) The taxi company has a policy that any taxi with mileage more than 1.95 standard deviations above the mean should be removed from the road and inspected. What is the probability that a randomly selected taxi from the fleet will have to be inspected?
d) A randomly selected taxi in the fleet traveled 20.6 thousand miles in the last year. Should this taxi be removed from the road and inspected? Explain why or why not.
a) Distance traveled per taxi per year in its entire fleet is normally distributed
X ~ N(12, 4)
z = (7 - u)/s
z = (7 - 12)/4
z = -5/4
z = -1.25
b) The z-score tells us that the taxi has traveled 1.25 standard deviations below the mean distance traveled by all the taxis in its entire fleet
c) We need to find:
P(z > 1.95)
= 1 - P(z < 1.95)
= 1 - 0.9744
d) X = 20.6
z = (20.6 - 12)/4
z = 8.6/4
z = 2.15
This means that the taxi has traveled 2.15 standard deviations above the mean. As it is above the 1.95 standard deviations above the mean, it should be removed from the road and inspected
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