The scores for a standardized reading test are found to be n

The scores for a standardized reading test are found to be normally distributed with a mean of 200 and a standard deviation of 20. If the test is given to 900 students, how many are expected to have scores between 200 and 220? 307 429 459 612

Solution

Given,

Standard Deviation = 20

Mean = 200

Number of test given = 900

Formula Used:

Z score (z) = (Test Score - Mean)/Standard deviation

First, lets find the z score for 200.

z = (200-200)/20 = 0

Now, lets find the z score for 220.

z = (220-200)/20 = 1.

Find P(Z < 1) And P(Z < 0)

P(Z < 1) = 0.8413 ----1

.P(Z < 0) = 0.500 ----2

Subtract equation 1 and 2

  0.8413 - 0.5000 = 0.3413

Multiply this difference percentage by 900.

0.3413 X 900 = 307.17

After rounding off, we get 307 students.

So, 307 students are expected to get scores between 200 and 220

Therefore, Option A is correct.