Question

Assume that hybrid zation experiments are cenducted with peas havig the properly that for offepring, there is a 0.75 probability that a pea has green pods. Assume hat the offepring peas are randomly selected in greups o 20. Comolete parts (a) through (e) below a. Find the mean and the standard deviation for the numbers of peas with green pods in the groups of 20 The value of the mean isp (Type en integer or a decimal. Do not round.) The: vali.e nt the standard deviaton is peas. (Raund ta ona dacimal place as roadod b. Use the range rule of thumb lo find the values separating reeuts thal a Velues ofpees or fewer ere significanty low. Raund ta one decimal place as Values pe or greater are eignfcanly high Round to c. Is a result of 7 peas wth green pods a rasult that s significanty?Why or why not? The resultnifcantly kaw, because peas with green pods is (Raund to ona dacimel place as noaded ere significantly low or significanty higt readed one decimal place as reeded

Answer 1

a.

Given, n = 20, p = 0.75

The value of the mean is $\mu$ = np = 20 * 0.75 = 15

The value of standard deviation is, $\sigma = \sqrt{np(1-p)} = \sqrt{20 * 0.75 * (1 - 0.75)}$ = 1.9

b.

According to the range rule of thumb, most values should lie within 2 standard deviations of the mean.

Lower limit = 15 - 2 * 1.9 = 11.2

Value of 11.2 peas or fewer are significantly low.

Upper limit = 15 + 2 * 1.9 = 18.8

Value of 18.8 peas or greater are significantly high.

As, the value 7 lies below the lower limit of 11.2,

The result is significantly low because 7 peas with green pods is less than 11.2 peas.