Elementary Statistic

Question

A study was conducted to determine whether there were significant differences between medical students admitted through special programs (such as retention incentive and guaranteed placement programs) and medical students admitted through the regular admissions criteria. It was found that the graduation rate was 90.9% for the medical students admitted through special programs. (Round all answers to 4 decimal places)

a) If 10 of the students from the special programs are randomly selected, find the probability that at least 9 of them graduated.

prob = 

b) If 10 of the students from the special programs are randomly selected, find the probability that exactly 7 of them graduated.

prob = 

c) Would it be unusual to randomly select 10 students from the special programs and get exactly 7 that graduate?

1. yes, it is unusual
2. no, it is not unusual

d) If 10 of the students from the special programs are randomly selected, find the probability that at most 7 of them graduated.

prob = 

e) Would it be unusual to randomly select 10 students from the special programs and get at most 7 that graduate?

1. yes, it is unusual
2. no, it is not unusual

Answer 1

Hi,

Here we use the Binomial Probability Function: 

P(X = x) = n! / ((n-x)! x!)(p)^x(q)^n-x

where X is is our random variable which represents the number of students graduating

n = 10 the sample size

p = .909 the probability of success (students graduate)

q = .091 the probability of failure

a) P(X ≥ 6) = P(X = 6) + P(X = 7) + P(X = 8) + P(X = 9) + P(X = 10) = 10! / (10-6)! 6!(.909)⁶(.091)^10-6+ 10! / (10-7)! 7!(.909)⁷(.091)^10-7+10! (10-8)! 8!(.909)⁸(.091)^10-8...10! (10-10)! 10!(.909)¹⁰(.091)^10-10

I'll let you attempt this on your own first, but let me know if you have any questions and I would be happy to go into more detail!

b) To find the probability of an exact number of students graduating, you can use the same formula.

P(X = 7) = 7! / (10-7)! 7!(.909)⁷(.091)^10-7

c) For this question, you are being asked to interpret your answer to the previous question. You should get a very small value, which tells you that it is unusual for exactly 7 students to graduate.

d) This question is similar to part a, but this time you are being asked to find the probability of at most 7 graduated. The phrase "at most" implies that you should solve for P(X ≤ 7) using the same method that you did in part a. P(X ≤ 7) = P(X = 7) + P(X = 6) + P(X = 5) + P(X = 4) + P(X = 3)+P(X = 2) +P(X = 1)

e) For this question, you are being asked to interpret your answer to the previous question. If you get a very small value, this tells you that it is unusual for this event to occur. On the other hand, if you get a very large value, this tells you that the event is not unusual.

Let me know if you have any questions! Hope this helped!