Question

Speeding: On a stretch of Interstate-89, car speed is a normally distributed variable with a mean of 69.1 mph and a standard deviation of 3.3 mph. You are traveling at 73 mph. Approximately what percentage of cars are traveling faster than you? Enter your answer as a percentage with 1 decimal place.

Answer 1

Answer: 11.9%

Step-by-step explanation:

Given :  On a stretch of Interstate-89, car speed is a normally distributed variable with $\mu=69.1$ mph and $\sigma=3.3$ mph.

Let x be a random variable that represents the car speed.

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

z-score corresponds x = 73 , $z=\dfrac{73-69.1}{3.3}\approx1.18$

Required probability :

$\text{P-value }: P(x>73)=P(z>1.18)\\\\=1-P(z<1.18)\\\\1-0.8809999\\\\=0.1190001=11.90001\approx11.9\%$

[using z-value table.]

Hence, the approximate percentage of cars are traveling faster than you = 11.9%