Almost all medical schools in the United States require applicants to take the M

Question

Almost all medical schools in the United States require applicants to take the Medical College Admission Test (MCAT). On one exam, the scores of all applicants on the biological sciences part of the MCAT were approximately Normal with mean 9.2 and standard deviation 2.6. For applicants who actually entered medical school, the mean score was 10.7 and the standard deviation was 1.4.

What percent of all applicants had scores higher than 12?

What percent of those who entered medical school had scores between 8 and 11?

Please show work.

Explanation / Answer

From information given, Xi=12, Xbar=9.2 and s=2.6. Substitute the values to obtain the z scoree.

z=(Xi-Xbar)/s=(12-9.2)/2.6=1.08

Find area beyond z=1.08 and multiply with 100 to obtain the required percent. Answer is 14.01%.

Find z scores corresponding to Xi=8 and 11.

z1=(8-10.7)/1.4=-1.93 and z2=(11-10.7)/1.4=0.21

Find areas corresponding to respective z scores:0.4732 and 0.0832. Add the areas and multiply with 100 to get the required percenatge. Ans: (0.4732+0.0832)*100=55.64%.

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