The data in a data set are normally distributed with a mean

The data in a data set are normally distributed with a mean of 170 and a standard deviation of 20. Estimate the percent of the data that are less than 150 or greater than 190.

Solution

Let the random variable X represent the distribution given in the problem. We have,

X~N(170,20²)

Using the empirical rule we know that 68% of the data lies within one standard deviation from the mean. 150 is one standard deviation less than the mean(150=170-20). Also 190 is one standard deviation greater than the mean(190=170+20)

Hence 68% of data will lie between 150 and 190. Hence the percent of data which does not lie between 150 and 190 or in other terms less than 150 or greater than 190 would be given by

P = (100-68)% = 32%