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.)

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.

Step-by-step 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.

x= -3 and

step-by-step explanation:

to find the roots of a cubic, use division or factoring to find the factors then set equal to 0. as this is a difference of cubes, it factors into

where a is the cube root of .

here   this is 27 and the cube root of 27 is 3. so we write using the form:

.

set each factor to 0 and solve for x.

x-3=0

x=3

the quadratic expression does not factor and must be solved using the quadratic formula.

where a = 1, b=3, and c=9

this cubic has two complex roots.

care to share were the trapezoid shown is ?