The mathematics section of a standardized college entrance exam had a mean of 22.522.5 and an SD of 5.15.1 for a recent year.

Question

The mathematics section of a standardized college entrance exam had a mean of

22.522.5

and an SD of

5.15.1

for a recent year. Assume these are well modeled by a Normal distribution.

​a) About what percent of students scored over

3333​?

​b) About what percent of students scored under

1616​?

​c) About what percent of students scored between

1616

and

3333​?

Answer 1

I don't really understand your number designations that appear to have two decimal points (22.522.5 and 5.15.1.) but the only thing that seems to make sense to me is a mean of 2252.25 and a standard deviation of 515.1 so I'll proceed based on that.

Based on a standard normal distribution, this represents the problem. The percentages in each major section are shown, but as you can see, the scores in question do not fall on even standard deviation increments (z-scores).

If you have a TI-84 calculator, you would just use to normalcdf function (select "distr", the 2 on the menu).

For question a), use a lower limit of 3333 and an upper limit of 1x10⁹⁹ (type 1, then the EE button, then type 99), the mean (μ) = 2252.25, the standard deviation (σ) = 515.1, then paste it into the function and push enter. The result is 1.79%

For question b), use a lower limit of 1x10^-99 and an upper limit of 1616, the mean (μ) = 2252.25, the standard deviation (σ) = 515.1, then paste it into the function and push enter. The result is 10.84%

For question c), use a lower limit of 1616 and an upper limit of 3333, the mean (μ) = 2252.25, the standard deviation (σ) = 515.1, then paste it into the function and push enter. The result is 87.37%