Question

1. We gave a national verbal proficiency test that has a mean of 500 and a standard deviation of 75.

How many, out of the 1500 subjects we tested, are likely to score above 400 on this test?

2. We gave a national verbal proficiency test that has a mean of 500 and a standard deviation of 75.

What raw score on this test is so low that it would occur 5 % of the time or less?

Answer 1

Que.1

Probability of getting score more than 400 is 0.9082, Now we find how many students get score more than 400

1500 *0.9082 = 1362.3

It means 1362 students out of 1500 students get score more than 400.

Que.2

Here we have to find 5th percentile. There are 5% observations less than 5th percentile.

For standard normal distribution 5th percentile is

P(z < P5) = P( z < -1.64) = 0.05

We know that,

Hence score below 377 is occur 5% of time or less.