Changing the mean of a Normal distribution by a moderate amo

Changing the mean of a Normal distribution by a moderate amount can greatly change the percent of observations in the tails.
Suppose that a college is looking for applicants with SAT math scores 750 and above.

30.In 2010, the scores of men on the math SAT followed the N (534, 118) distribution. What percent of men scored 750 or better?

31.Women\'s SAT math scores that year had the N (500, 112) distribution. What percent of women scored 750 or better?

Please show steps so I understand how to do it.

Solution

To find these areas you either need a table for the normal distribution which you can use after you standardize the numbers from the distributions given in (A) and (B), or use a calculator with built-in stats functions, like a TI-83 or 84.

To standardize a value you subtract the mean and divide by the standard deviation. For a score of 750 in part (A) that gives z = (750 - 534) / 118 = 1.83050.

The area to the right of 1.83050 under the standard normal distribution is .0305 rounded to 4 decimal places. So the percent is 3.05%.

A similar calculation in part (B) gives

((750 - 500) / 112 = 2.2321

3.21%.