Question

Let x be a random variable that represents the commute time of teachers in a large urban area. If x is normally distributed with a mean of 46 minutes and a standard deviation of 5 minutes, find the commute time which is at the top of the bottom 25%.

Answer 1

Let X be a random variable that represents the commute time of teachers in a large urban area.

The random variable X is normally distributed with mean 46 minutes and standard deviation 5 minutes.

i.e, X~N(46,5)

We need to find the commute time which is at the top of the bottom 25%.

Let, t be the commute time which is at the top of the bottom 25%.

Then,

From the standard normal table we get,

The commute time is 42.6275512 minutes.