Question

A new variety of turf grass has been developed for use on golf courses, with the goal of obtaining a germination rate of 80%. To evaluate the grass, 20 seeds are planted in a greenhouse so that each seed will be exposed to identical conditions. If the 80% germination rate is correct, calculate the probabilities below. [6 points] a. What probability distribution model would be appropriate for describing the number of grass seeds that will germinate. Explain. b. What is the probability that exactly 17 seeds will germinate? c. Calculate the probability that less than 15 seeds will grow. d. What is the probability that more than 14 seeds will grow?

Answer 1

a. Binomial Distribution for germination of grass seeds.

b. P(exactly 17 germinate) = 0.0236695.

c. P(less than 15 germinate) = 0.418636.

d. P(more than 14 germinate) = 0.581364.

Step-by-step explanation:

a. The appropriate probability distribution model for describing the number of grass seeds that will germinate would be the Binomial Distribution.

This distribution is used to model the number of successes (germinated seeds) in a fixed number of trials (20 seeds), where each trial has a constant probability of success (80% in this case).

b. The probability that exactly 17 seeds will germinate can be calculated as:

P(exactly 17) = (20 choose 17) * (80/100)^17 * (20/100)^3

= 0.0236695

c. The probability that less than 15 seeds will grow can be calculated as:

P(less than 15) = 1 - P(exactly 15 or more)

= 1 - (20 choose 15) * (80/100)^15 * (20/100)^5

= 0.418636

d. The probability that more than 14 seeds will grow can be calculated as:

P(more than 14) = P(exactly 15 or more)

= (20 choose 15) * (80/100)^15 * (20/100)^5

= 0.581364

Hence, the appropriate probability distribution is Binomial Distribution, the probability that exactly 17 seeds is 0.0236695 , the probability that less than 15 seeds will grow is 0.418636 and probability that more than 14 seeds will grow is 0.581364.