Question

The speed at which cars travel on the highway has a normal distribution with a mean of 60 km/h and a standard deviation of 5 km/h.
What is the probability that a randomly chosen car traveling on this highway has a speed between 63 km/h and 75 km/h?

Answer 1

The z-score of the speed value gives the measure of dispersion of the from

the mean observed speed.

The probability that the speed of a car is between 63 km/h and 75 km/h is

0.273.

The given parameters are;

The mean of the speed of cars on the highway, $\overline x$ = 60 km/h

The standard deviation of the cars on the highway, σ = 5 km/h

Required:

The probability that the speed of a car is between 63 km/h and 75 km/h

Solution;

The z-score for a speed of 63 km/h is given as follows;

$Z=\dfrac{x-\bar x }{\sigma }$

Which gives;

$Z=\dfrac{63-60 }{5 } = 0.6$

From the z-score table, we have;

P(x < 63) = 0.7257

The z-score for a speed of 75 km/h is given as follows;

$Z=\dfrac{75-60 }{5 } = 3$

Which gives, P(x < 75) = 0.9987

The probability that the speed of a car is between 63 km/h and 75 km/h is therefore;

P(63 < x < 75) = P(x < 75) - P(x < 63) = 0.9987 - 0.7257 = 0.273

The probability that the speed of a car is between 63 km/h and 75 km/h is

0.273.

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