Question

Assume that hybridization experiments are conducted with peas having the property that for offspring, there is a 0.75 probability that a pea has green pods. Assume that the offspring peas are randomly selected in groups of 20.

Answer 1

Given:

probability = p = 0.75

sample size = no. of peas = n = 20

A.) The mean of a binomial distribution is the product of the sample size n and the probability p.

`\text{ }\mu\text{ = np}`

We get,

`\text{ }\mu\text{ = \lparen20\rparen\lparen0.75\rparen = 15}`

Therefore, the mean is 15.

B.) The standard deviation of a binomial distribution is the square root of the product of the sample size, n, and the probability, p.

`\text{ }\sigma\text{ = }√(npq)\text{ = }\sqrt{np(1\text{ - p\rparen}}`

We get,

`\text{ }\sigma\text{ = }\sqrt{20(0.75)(1\text{ - 0.75\rparen}}`
`\text{ }\sigma\text{ = 3.75}`

Therefore, the standard deviation is 3.75