In a certain university, math SAT scores for the entering freshman class averaged 650 and had a standard deviation of 100. The maximum possible score is 800. Is it possible that the scores of these freshmen are normally distributed? Explain.

Answer:

Step 1 of 1:

In this question, we are asked to find the possibilities that the scores of these freshmen are normally distributed.

Mean of scores = 650, standard deviation = 100.

The maximum possible score is 800.

Lets plot the normal probability density function with mean and standard deviation .

Figure 1: PDF of a normal random variable with mean and variance .

From the figure we can see that the normal curve is symmetric around mean .

There are three cases for any given normal population from the normal curve.

About 68% of the population is in the interval

About 95% of the population is in the interval

About 99.7% of the population is in the interval

Lets come to question where maximum possible score is 800, mean 650 and standard deviation 100.

Since 99.7% of the population is in the interval

So maximum possible score should be 950, but in the question value of maximum possible score is 800.

Since value of score is truncated up to 800.

we can conclude that the scores of these freshmen are not normally distributed.