Question

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

The percentage of the cars that are going faster than 75 mph is______ %.

Answer 1

Solution:

Given: Speeds of automobiles on a certain stretch of freeway at 11:00 PM are normally distributed with mean 65 mph.

Mean = 65

We are given:

P( 55 < X < 65) = 18%

Since 65 is mean, P( X< 65) = 50%

then

P( 55 < X < 65) = 18%

P( X < 65) - P( X< 55 )  = 18%

50% - P( X< 55 )  = 18%

50% - 18 % = P( X< 55 )  

that is:
P( X< 55 )  = 32%

We have to find: the percentage of the cars that are going faster than 75 mph .

P( X > 75) = ...........?

Since X = 55 and X = 75 are at same distance from mean 65 and Normal distribution is symmetric around the mean value,

P( X < 55) = P( X > 75) = 32%

thus

The percentage of the cars that are going faster than 75 mph is 32%