Ch. 6.1 #7-49 odd

q = 1–q = 1 – 0.6 = 0.4
np = (10)(0.6) =6
nq = (10)(0.4) = 4
No because np ≥ 5 and nq ≤ 5.
c. n=40, p=0.9
q = 1–q = 1 – 0.9 = 0.1
np = (40)(0.9) =36
nq = (40)(0.1) = 4
No because np ≥ 5 and nq ≥ 5.
d. n=50, p=0.2
q = 1–q = 1 – 0.2 = 0.8
np = (50)(0.2) =10
nq = (50)(0.8) = 40
Yes, because np ≥ 5 and nq ≥ 5..
7. Percentage of Americans Who Have Some College Education The percentage of Americans 25
years or older who have at least some college education is 53.1%. In a random sample of 300 Americans
25 years old or older, what is the probability that more than 175 have at least some college education?
n=300, p=0.531
q = 1–q = 1 – 0.531 = 0.469
Since np = (300)(0.531) = 159.3 and nq = (300)(0.469) = 140.7, the normal distribution can be used to
approximate the binomial distribution (np ≥ 5 and nq ≥ 5).
µ = np = (300)( 0.531) = 159.3
σ = npq = (300)(0.531)(0.469) 8.64
For binomial distribution, P(X >175)
For normal distribution, P(X >175 + 0.5) = P(X > 175.5)