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 10. 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 10.
μ=___ peas.
(Type an integer or a decimal. Do not round.)
The value of the standard deviation is
σ=___peas.
(Round to one decimal place as needed.)
b. Use the range rule of thumb to find the values separating results that are significantly low or significantly high.
Values of ___ peas or fewer are significantly low.
(Round to one decimal place as needed.)
Values of ___ peas or greater are significantly high.
(Round to one decimal place as needed.)
c. Is a result of 2 peas with green pods a result that is significantly low? Why or why not?
The result (is, is not) significantly low, because 2 peas with green pods is (greater than, equal to, less than) peas.
(Round to one decimal place as needed.)

Answer 1

a.

Mean = 7.5

Standard Deviation = 1.4

b.

Values of 4.8 peas or fewer are significantly low.

Values of 10.2 peas or fewer are significantly high

c.

The result is significantly low, because 2 peas with green pods is less than 4.8 peas.

Explanation:

Given

n = 10

p = 0.75

a. Calculating mean and Standard deviation

The mean of a binomial distribution is the product of the sample size and the probability

Mean = np

Mean = 10 * 0.75

Mean = 7.5

Calculating standard deviation

The standard deviation of a binomial distribution is the product of the sample size and the probability p and q

where q = 1 - p

q = 1 - 0.75

q = 0.25

σ = √npq

σ = √(10 * 0.75 * 0.25)

σ = 1.36930639376291528364242

σ = 1.4 --- Approximated

b.

Using rule of thumb;

The rule of thumb tells us that the usual range of values is 2 within the standard deviation of the mean

i.e u ± 2σ

u - 2σ = 7.5 - 2(1.369) = 4.762 = 4.8

u + 2σ = 7.5 + 2(1.369) = 10.238 = 10.2

c. The result is significantly low, because 2 peas with green pods is less than 4.8 peas.