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%.