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 26. complete parts (a) through (c) below.
a. find the mean and the standard deviation for the numbers of peas with green pods in the groups of 26.
the value of the mean is μ = peas.
(type an integer or a decimal. do not round.)

Explanation:

Step1: Identify the distribution

This is a binomial distribution problem, where $n = 26$ (number of trials, i.e., number of peas) and $p=0.75$ (probability of a pea having green pods).

Step2: Calculate the mean

The formula for the mean of a binomial distribution is $\mu = np$. Substitute $n = 26$ and $p = 0.75$ into the formula: $\mu=26\times0.75 = 19.5$.

Step3: Calculate the standard - deviation

The formula for the standard deviation of a binomial distribution is $\sigma=\sqrt{np(1 - p)}$. First, find $1-p=1 - 0.75=0.25$. Then, $np(1 - p)=26\times0.75\times0.25 = 4.875$. So, $\sigma=\sqrt{4.875}\approx2.2079$.

Answer:

The value of the mean is $\mu = 19.5$ peas.