Ch. 6.1 #7-49 odd

11. Elementary School Teachers Women comprise 80.3% of all elementary school teachers. In a
random sample of 300 elementary teachers, what is the probability that more than three-fourths are
women?
n=300, p=0.803
q = 1–q = 1 – 0.803= 0.197
Since np = (300)(0.803) = 240.9 and nq = (300)(0.197) = 59.1, the normal distribution can be used to
approximate the binomial distribution (np ≥ 5 and nq ≥ 5).
µ = np= (300)(0.803) = 240.9
σ = npq = (300)(0.803)(0.197) 6.89
For binomial distribution, P(X >225) ¾ (300)=225
For normal distribution, P(X >255 + 0.5) = P(X > 255.5)
240.9 255.5
The z value is z = 225.5 240.9 2.24 area=0.0125
6.89
P(z > 225.5)=P(X > -2.24)=1- 0.0125 =0.9875 or 98.75%