Problem 10BSC

Mendelian Genetics When Mendel conducted his famous genetics experiments with peas, one sample of offspring consisted of 580 peas, and Mendel theorized that 25% of them would be yellow peas.

a. If Mendel’s theory is correct, find the mean and standard deviation for the numbers of yellow peas in such groups of 580 offspring peas.

b. The actual results consisted of 152 yellow peas. Is that result unusually high? What does this result suggest about Mendel’s theory?

Answer :

Step 1:

Given, when Mendel conducted his famous genetics experiments with peas, one sample of offspring consisted of 580 peas, and Mendel theorized that 25% of them would be yellow peas.

Here, n = 580, and p = 25% = 0.25, q = 1-p = 1 - 0.25 = 0.75.

a). We have to find the mean and standard deviation for the numbers of yellow peas in such groups of 580 offspring peas.

That is,

Mean μ = np = 5800.25 = 145.

Variance = npq = 580(0.25)(0.75) = 108.75.

And standard deviation = = =