Question

The speeds of cars on a given i street we are normally distributed with a mean of 72 miles per hour and a standard deviation of 3.2 miles per hour. What percent of drivers are traveling between 70 and 80 miles per hour based on this distribution

Answer 1

Answer: 72.78% of the drivers are traveling between 70 and 80 miles per hour based on this distribution.

Explanation:

Let X be a random variable that represents the speed of the drivers.

Given: population mean : M = 72 miles ,

Standard deviation: s= 3.2 miles

The probability that the drivers are traveling between 70 and 80 miles per hour based on this distribution:

`P(70\leq X\leq 80)=P((70-72)/(3.2)\leq (X-M)/(s)\leq(80-72)/(3.2))\\\\= P(-0.625\leq Z\leq 2.5)\ \ \ \ \ [Z=(X-M)/(s)]\\\\=P(Z\leq2.5)-P(Z\leq -0.625)\\\\\\ =0.9938-0.2660\ \ \ [\text{Using p-value calculator}]\\\\=0.7278`

Hence, 72.78% of the drivers are traveling between 70 and 80 miles per hour based on this distribution.