Question

The commute times (amounts of time it takes people to commute from home to work) for people who live in a large city are bell-shaped with a mean of 65 minutes and a standard deviation of 9 minutes.

Using the Empirical Rule, what is the approximate percentage of commute times in this distribution that are greater than 83 minutes?

Answer 1

Solution :

Given that,

= 65

= 9

Using Empirical rule,

P( - 2< X < + 2) = 95%

P(65 - 2 * 9 < X < 65 + 2 * 9) = 95%

P(65 - 18 < X < 65 + 18) = 95%

P(47 < X < 83) = 95%

The approximate percentage of commute times in this distribution that are greater than 83 minutes is,

P(X > 83) = 2.5%

Answer = 2.5%