Question

Almost all medical schools in the United States require students to take the Medical College Admission Test (MCAT). A new version of the exam was introduced in spring 2015 and is intended to shift the focus from what applicants know to how well they can use what they know. One result of the change is that the scale on which the exam is graded has been modified, with the total score of the four sections on the test ranging from 472 to 528 . In spring 2015 the mean score was 500.0 with a standard deviation of 10.6 .What proportion of students taking the MCAT had a score over 512

Answer 1

Answer:

12.92%

Step-by-step explanation:

Mean of the scores= u = 500

Standard deviation = $\sigma$ = 10.6

We have to find what proportion of students scored more than 512 marks.

The distribution of scores in a test generally follows the Normal distribution. So we can assume that the distribution of MCAT scores is normally distributed about the mean.

Since, the distribution is normal, we can use the concept of z scores to find the proportion of students who scored above 512.

The formula for z scores is:

$z=\frac{x-u}{\sigma}$

So, z score for x = 512 will be:

$z=\frac{512-500}{10.6}=1.13$

Thus,

P(X > 512) is equivalent to P(z > 1.13)

So, the test scores of 512 is equivalent to a z score of 1.13. Using the z table we have to find the proportion of z scores being greater than 1.13, which comes out to be 0.1292

Since,

P(X > 512) = P(z > 1.13)

We can conclude that, the proportion of students taking the MCAT who had a score over 512 is 0.1292 or 12.92%