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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 . Use Table A to find the answers to the two questions.

(a) What proportion of students taking the MCAT had a score over 519 ?
(b) Compute the proportion and then enter the answer as a percentage rounded to two decimal places.

Respuesta :

Answer:

(a) The proportion of students taking the MCAT had a score over 519 is 0.0367.

(b) The percentage of students who scored more than 519 in the MCAT is 3.67%.

Step-by-step explanation:

Assuming that the sample size or the number of students taking the MCAT in 2015 is large, the sampling distribution of scores follow a normal distribution.

Let X = score of a student

Given:

Mean = [tex]\mu=500[/tex]

Standard deviation = [tex]\sigma=10.6[/tex]

(a)

Compute the probability of students who scored more than 519 as follows:

[tex]P(X>519)=P(\frac{X-\mu}{\sigma}> \frac{519-500}{10.6})\\=P(Z>1.7925)\\=1-P(Z<1.7925)[/tex]

Use the z-table to determine the probability.

[tex]P(X>519)=P(\frac{X-\mu}{\sigma}> \frac{519-500}{10.6})\\=P(Z>1.7925)\\=1-P(Z<1.7925)\\=1-0.9633\\=0.0367[/tex]

Thus, the probability of students who scored more than 519 is 0.0367.

(b)

Convert the probability of students who scored more than 519 to percentage

[tex]=0.0367\times100\\=3.67\%[/tex]

Thus, the percentage of students who scored more than 519 is 3.67%.

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