Question

Chpt 6
	A study by Stanford University concluded that 45% of college
	students sleep at least 8 hours per night. In a sample
	of 10 DCCC students, find the probability that
	at least 8 of the 10 get 8 or more.

Answer 1

Solution:

Here, we have to use binomial distribution formula for finding the required probability.

We are given

p = 0.45,

q = 1 – p = 1 – 0.45 = 0.55

n = 10,

We have to find P(X≥8)

P(X≥8) = P(X=8) + P(X=9) + P(X=10)

P(X=x) = nCx*p^x*q^(n – x)

P(X=8) = 10C8*0.45^8*0.55^(10 – 8)

P(X=8) = 45*0.45^8*0.55^2

P(X=8) = 0.02289

P(X=9) = 10C9*0.45^9*0.55^(10 – 9)

P(X=9) = 10*0.45^9*0.55^1

P(X=9) = 0.004162

P(X=10) = 10C10*0.45^10*0.55^(10 – 10)

P(X=10) = 1*0.45^10*0.55^0

P(X=10) = 0.000341

P(X≥8) = P(X=8) + P(X=9) + P(X=10)

P(X≥8) = 0.02289 + 0.004162 + 0.000341

P(X≥8) = 0.027393

Required probability = 0.027393