A gardener buys a package of seeds. Eighty-one percent of seeds of this type germinate. The gardener plants 120 seeds. Approximate the probability that the number of seeds that
Germinate is between 89.2 and 105.2 exclusive.
A) 0.0801
B) 0.0401
C) 0.9599
D) 0.9199

Question

Quizplus · Accepted Answer

To approximate the probability that the number of seeds that germinate is between 89.2 and 105.2 exclusive, we can use the normal distribution as an approximation to the binomial distribution since the sample size is large (n = 120). The mean (μ) of the distribution is n*p = 120*0.81 = 97.2, and the standard deviation (σ) is sqrt(n*p*(1-p)) = sqrt(120*0.81*0.19) ≈ 8.3. We convert the bounds to z-scores: z1 = (89.2-97.2)/8.3 ≈ -0.96 and z2 = (105.2-97.2)/8.3 ≈ 0.96. Looking up these z-scores in a standard normal distribution table or using a calculator, we find the probabilities corresponding to these z-scores and subtract them from 1 to find the probability in between. This calculation gives us a probability close to 0.9199, indicating that the probability the number of seeds that germinate is between 89.2 and 105.2 exclusive is approximately 91.99%.

A Gardener Buys a Package of Seeds