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
<u>0.273</u>.
The given parameters are;
The mean of the speed of cars on the highway,
= 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 }](https://tex.z-dn.net/?f=Z%3D%5Cdfrac%7Bx-%5Cbar%20x%20%7D%7B%5Csigma%20%7D)
Which gives;
![Z=\dfrac{63-60 }{5 } = 0.6](https://tex.z-dn.net/?f=Z%3D%5Cdfrac%7B63-60%20%7D%7B5%20%7D%20%3D%200.6)
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](https://tex.z-dn.net/?f=Z%3D%5Cdfrac%7B75-60%20%7D%7B5%20%7D%20%3D%203)
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
<u>0.273</u>.
Learn more here:
brainly.com/question/17489087