Question

A new version of the Medical College Admissions Test (MCAT) was introduced in spring 2015 and is intended to shift thie focu: 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 was 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. (a) Assuming that the MCAT scores are normally distributed, use Table A to find the median and the first and third quartiles of the MCAT scores. Find the median of the MCAT scores. (Enter your answer rounded to a whole number.) median = Find the first quartile of the MCAT scores. (Enter your answer rounded to three decimal places.) Find the first quartile of the MCAT scores. (Enter your answer rounded to three decimal places.)

Q1 Find the third quartile of the MCAT scores. (Enter-your answer rounded to three decimal places.)
Q3= Find the interquartile range of the MCAT scores. (Enter your answer rounded to three decimal places.) IQ

Answer 1

The median of MCAT scores is 500, the first quartile (Q1) is approximately 492.85, the third quartile (Q3) is approximately 507.15, and the interquartile range (IQR) is approximately 14.3.

Step-by-step explanation:

The question refers to determining the quartiles and interquartile range of the MCAT scores based on a normal distribution, where the mean score is 500.0 and the standard deviation is 10.6. In a normal distribution, the median is the same as the mean, hence the median is 500. The first and third quartiles correspond to the 25th and 75th percentiles, respectively.

Using the standard normal distribution, the z-score for the 25th percentile is approximately -0.675, and the z-score for the 75th percentile is approximately 0.675. These z-scores can be used in the formula:

Quartile = mean + (z-score * standard deviation)

For the first quartile (Q1):

• Q1 = 500.0 + (-0.675 * 10.6) ≈ 492.85

For the third quartile (Q3):

• Q3 = 500.0 + (0.675 * 10.6) ≈ 507.15

The interquartile range (IQR) is the difference between the third and first quartiles:

• IQR = Q3 - Q1 ≈ 507.15 - 492.85 ≈ 14.3