Question

The speed of cars on a stretch of road is normally distributed with an average 51 miles per hour with a standard deviation of 5.9 miles per hour. What is the probability that a randomly selected car is violating the speed limit of 50 miles per hour?

0.43

0.50

0.51

0.57

Answer 1

Answer: 0.57

Step-by-step explanation:

Given : The speed of cars on a stretch of road is normally distributed .

Population Mean = $\mu=51\text{ miles per hour}$

Standard deviation : $\sigma= 5.9\text{ miles per hour}$

Let x be the random variable that represents the speed of cars on a stretch of road .

z-score : $z=\dfrac{x-\mu}{\sigma}$

For x= 50.

$z=\dfrac{50-51}{5.9}\approx-0.17$

By using the standard normal distribution table ,

The probability that a randomly selected car is violating the speed limit of 50 miles per hour :-

$P(x>50)=1-P(x\leq50)=1-P(z\leq-0.17)\\\\=1- 0.4325051=0.5674949\approx0.57$