Question

The speed of cars on a stretch of road is normally distributed with an average 48 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? (a) 0.37 (b) 0.48 (c) 0.21 (d) 0.63

Answer 1

Answer: (a) 0.37

Step-by-step explanation:

Given: The speed of cars on a stretch of road is normally distributed with an average 48 miles per hour with a standard deviation of 5.9 miles per hour.

i.e. Mean : $\mu = 48\text{ miles per hour}$

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

The formula to calculate z is given by :-

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

For the probability that a randomly selected car is violating the speed limit of 50 miles per hour (X≥ 50).

For x= 80

$z=\dfrac{50-48}{5.9}=0.338983050847\approx0.34$

The P Value =$P(z>0.34)=1-P(z<0.34)=1-0.6330717\approx0.3669283\approx0.37$

Hence,  the probability that a randomly selected car is violating the speed limit of 50 miles per hour =0.37