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There are 8 questions on a true-false test. A student was unprepared for this te

ID: 3370020 • Letter: T

Question

There are 8 questions on a true-false test. A student was unprepared for this test and randomly guessed the answer for each of these questions.

(a) Why is the Binomial distribution applicable to this scenario? (Give 3 reasons)

1. _________________________________

2. _________________________________

3. _________________________________

With data: n = 8, p = 0.5, and q = 0.5

(b) What is the chance the student gets less than or equal to 5 correct? Use the Binomial formula to answer.

________________________________

(c) Write an Excel formula to answer question (b).

________________________________

Explanation / Answer

a)

b)
As per binomial distribution,
P(X=r) = nCr * p^r * (1-p)^(n-r)


P(x < =5) = P(x =0) =P(x =1) +P(x =2) +P(x =3) + P(x =4) + P(x =5)
= 8C0 * 0.5^0 * (1-0.5)^8 + 8C1 * 0.5^1 * (1-0.5)^7 + 8C2 * 0.5^2 * (1-0.5)^6 + 8C3 * 0.5^3* (1-0.5)^5 + 8C4 * 0.5^4 * (1-0.5)^4 + 8C5 * 0.5^5 * (1-0.5)^3


= 0.8555


c)
=BINOM.DIST(5,8,0.5,TRUE)