Question

Main Question: There is concern in the community that a particular group of students is getting preferential treatment when it comes to admittance to VCU. A random sample of 14 students who are a part of the particular group in question is examined and it is found that the average SAT score for these students is 1050. Is there a problem with this particular group of students?   Use the results from questions 1 and 2 to justify your answer.

This is question 1 & 2:

1. In 2019, the average SAT score for an admitted student to VCU was 1180 with a standard deviation of 160. If these times were normally distributed, what is the probability a student chosen at random will have a SAT score of less than 1050? Would this be unusual?

2. Using the information from problem 1, what is the probability that the average SAT score 14 random students will be less than 1050?

Answer 1

Here mean = mu = 1180 and std.dev. = sigma = 160

Here X= SAT score

P( X < 1050) we can calculate this probability using excel command as follows

=NORMDIST(1050,1180,160,1) = 0.208252 ( 0.208>0.05)

This probability is usual since this is greater than 0.05

Now sample size = 14

So new std.dev = original std.dev/sqrt(14) = 160/sqrt(14) = 42.7618

Xbar = average SAT score

P( Xbar < 1050)

we can calculate this probability using excel command as follows

=NORMDIST(1050,1180,42.7618,1) = 0.001183 here(0.00118<0.05)

This probability is unusual since it is less than 0.05

so for 14 student average 1050 have some problem since this probability is unusual