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 40.
a. What is the standard deviation?

b. What are the values separating results that are significantly low and significantly high?

Answer 1

Answer:

a) Standard Deviation = 2.74

b) Significantly Low = values below 24.52 (or equal)

Significantly High = values above 35.48 (or equal)

Step-by-step explanation:

This is binomial probability distribution problem.

Where n = 40 [groups of 40, total trials]

p = 0.75 [probability of success]

a)

The formula for standard deviation is:

$Standard \ Deviation = \sqrt{np(1-p)}$

We know  n = 40 and p = 0.75, so the standard deviation is:

$Standard \ Deviation = \sqrt{np(1-p)} \\Standard \ Deviation = \sqrt{(40)(0.75)(1-0.75)}\\ Standard \ Deviation = 2.74$

b)

the range rule of thumb tells us that usual range of values is within 2 standard deviation of the mean. First let's calculate mean.

We know,

Mean = n * p = 40 * 0.75 = 30

So

Mean - 2* Standard Deviation = 30 - 2(2.74) = 24.52

and

Mean + 2* Standard Deviation = 30 + 2(2.74) = 35.48

Significantly Low = values below 24.52 (or equal)

Significantly High = values above 35.48 (or equal)