Do not use any kind of software in this problem. Show all the details in your ca

Question

Do not use any kind of software in this problem. Show all the details in your calculations. It is known that approximately 55% of high school seniors score 21 or more on the Math portion of the ACT. Suppose you select 15 high school seniors (who took the ACT) from a local high school.

(a) What is the probability that exactly 5 of them scored 21 or more?

(b) What is the probability that none of them scored 21 or more?

(c) What is the probability that at least one scored 21 or more? Hint: use the answer from part (b).

(d) Calculate the expected value (mean) and standard deviation of X, the number of high school seniors who scored 21 or more on the Math portion of the ACT.

Explanation / Answer

p = .55

n=15

We will use the binomial distribution to solve the problem

a. P(X=5,15) = 15C5(.55^5)(.45^10) = 0.05146

b. P(X=0,15) = 15C0(.55^0)(.45^15) = 6.28*10^-6

c. P(X>=1) = 1-P(X=0) = 1-6.28*10^-6 = .99999372

d. Expected value = np = .55*15 = 8.25

Standard deviation = sqrt(npq) = sqrt(15*.55*45) = 1.93

Related Questions

Navigate

• Browse (All)
• Browse D
• Subjects

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.