Question

The speed limit on a road is 60 mph. The actual speeds of cars are measured and found to be normally distributed with a mean value of 63 mph and a standard deviation of 5 mph. Approximately what percentage of cars exceed the speed limit by more than 10 mph?
A) 5.0%
B) 6296%
C) 7.3%
D) 8.1%

Answer 1

Answer:  8.1%

Step-by-step explanation:

Given : $\mu=63$

$\sigma=5$

Let x be the random variable that represents the actual speeds of cars.

The speed limit on a road is 60 mph.

Using formula , $z=\dfrac{x-\mu}{\sigma}$, we have for x= 60+10=70

$\dfrac{70-63}{5}=1.4$

Using z-table for right-tailed test value, The probability of  cars exceed the speed limit by more than 10 mph will be

$P(x>70)=P(z>1.4)=0.0807567\approx0.081=8.1\%$

Hence, the percentage of cars exceed the speed limit by more than 10 mph is 8.1%.