Help with a statistics problem

Question

. Gardening: A gardener buys a package of seeds. Eighty percent of seeds of this type germinate. The gardener plants 90 seeds.

a.	Approximate the probability that fewer than 75 seeds germinate.

Answer 1

x = number of seeds that germinate

trying to find P(x < 75)

Use normal approximation of binomial distribution to solve this problem:

mean = np = 90 * 0.8 = 72

standard deviation = sqrt(npq) = sqrt (90*0.8*0.2)=3.795

Compute z-stat so can use standard normal probability table:

z = (x -mean)/std dev

z = (75 - 72) / 3.795 = 0.79

Find P(z < 0.79) from standard normal probability table = 0.7852