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

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=(x-\mu)/(\sigma)`

For x= 50.

`z=(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\\`