Question

SAT verbal scores are normally

distributed with a mean of 450

and a standard deviation of 120.

Determine what percent of the

scores lie between 450 and 570.

Answer 1

The percentage of the scores lying between 450 and 750 is 49.4%

Explanation:

In this question, we are simply asked to calculate the percentage of the scores lying between a particular range.

The first thing to do here is to calculate the z score of both scores

Mathematically, z score = (x - mean)/SD

for score 450, we have ; z = (450-450)/120 = 0/120 = 0

For score 750, we have z = (750-450)/120 =

2.5

Now, we move on to calculate the probability before turning it into a percentage.

The supposed probability we are to calculate is as follows;

P(450 < x < 750) or P(0 < z < 2.5)

Using standard score table, P = 0.49379

The percentage is thus 49.4%