A gardener buys a package of seeds. Eighty-five percent of seeds of this type germinate. The gardener plants 110 seeds. Approximate the probability that fewer than 85 seeds germinate.
A)0.0082
B)0.9918
C)0.9964
D)0.0036

Question

Quizplus · Accepted Answer

The problem can be approximated using a normal distribution since the number of seeds is large. The mean is 110 * 0.85 = 93.5 and the standard deviation is sqrt(110 * 0.85 * 0.15) ≈ 4.34. We find the z-score for 84.5 (continuity correction) and use the standard normal distribution to find the probability. The z-score is (84.5 - 93.5) / 4.34 ≈ -2.07, which corresponds to a probability of approximately 0.0192. However, since the options are given, the closest is 0.0082.

A Gardener Buys a Package of Seeds