Question

A radar unit is used to measure speeds of cars on a motorway. the speeds are normally distributed with a mean of 90 km/hr. and a standard deviation of 10 km/hr. what is the probability that a car picked at random is travelling at more than 100 km/hr.

Answer 1

The probability is 0.1587.

The z-score associated with this is found using the formula

z = (X-μ)/σ = (100-90)/10 = 10/10 = 1.0

Using a z-table (http://www.z-table.com) we see that the area to the left of, less than, this is 0.8413.  We want the area greater than, so we subtract from 1:
1 - 0.8413 = 0.1587