Suppose that 3 of the 2 million high school students who tak

Suppose that 3% of the 2 million high school students who take the SAT each year receive special accommodations because of documented disabilities. Consider a random sample of 15 students who have recently taken the test. (Round your probabilities to three decimal places.) (a) What is the probability that exactly 1 received a special accommodation? (b) What is the probability that at least 1 received a special accommodation? (c) What is the probability that at least 2 received a special accommodation? (d) What is the probability that the number among the 15 who received a special accommodation is within 2 standard deviations of the number you would expect to be accommodated? (e) Suppose that a student who does not receive a special accommodation is allowed 3 hours for the exam, whereas an accommodated student is allowed 4.5 hours. What would you expect the average time allowed the 15 selected students to be? (Round your answer to two decimal places.) You may need to use the appropriate table in the Appendix of Tables to answer this question.

Solution

Here population is large prob is small but their product is finite.

There are independent trials and outcomes are 2.

Hence X = no of persons getting accommodation follow a Binomial distribution with p = 0.03 and n =15

a) P(x=1) = 0.2938

b) P(X>=1) = 0.3667

c) P(X>=2) = 0.0730

d) P(|x|<=mu-rtnpq)

i.e. mu = 15(0.03) = 0.45 and std dev = 0.1774

0.273<x<0.62 is P(X=0) = 0.6333