Use technology to solve the following problem: A gardener buys a package of seeds. Seventy-four percent of seeds of this type germinate. The gardener plants 120 seeds. Approximate the probability That the number of seeds that germinate is between 85.8 and 98.8 exclusive.
A) 0.9760
B) 0.3254
C) 0.6746
D) 0.3014

Question

Quizplus · Accepted Answer

We can use a binomial distribution (as each seed either germinates or doesn't) with n=120 and p=0.74 (probability of germination). Then, we can use the normal approximation to the binomial distribution, with mean=np=88.8 and standard deviation=sqrt(np(1-p))=6.95. Then, we standardize the values to find the corresponding z-scores:

z1=(85.8-88.8)/6.95=-0.43
z2=(98.8-88.8)/6.95=1.44

Using a standard normal distribution table or calculator, we can find the area under the curve between these z-scores to be approximately 0.6746, which is the probability that the number of seeds that germinate is between 85.8 and 98.8 exclusive. Therefore, the answer is choice C.

Use Technology to Solve the Following Problem: a Gardener Buys