Question

Speeds of automobiles on a certain stretch of freeway at 11:00 pm are normally distributed with mean 65 mph. Twenty percent of the cars are travelling at speeds between 55 and 65 mph. What percent of the cars are going faster than 75 mph?

Answer 1

Normal distribution is symmetry distribution. In that mean is at the middle, so half of the values are in the left of it and half of it in the right of it and all are symmetry.

So, half of the values (50%) are in the left of 65 mph. or we can say that 50% cars are travelling slower than 65 mph.

Now it is given that, there are 20% cars between 55 and 65 mph so by using symmetry there are 20% cars between 65 and 75 mph.

Since 50% cars are less than 65 mph, and there are 20% cars between 65 and 75 mph hence total (50+20=) 70% cars are slower than 75 mph.

So, 30% cars are faster than 75 mph.

In this we have used symmetry property of the normal distribution.