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 36. 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 36. The value of the mean is muequals 27 peas. ​(Type an integer or a decimal. Do not​ round.) The value of the standard deviation is sigmaequals 2.6 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 21.8 peas or fewer are significantly low. ​(Round to one decimal place as​ needed.) Values of 32.2 peas or greater are significantly high. ​(Round to one decimal place as​ needed.) c. Is a result of 15 peas with green pods a result that is significantly​ low? Why or why​ not? The result ▼ is not is significantly​ low, because 15 peas with green pods is ▼ less than equal to greater than nothing peas. ​(Round to one decimal place as​ needed.)

Answer 1

Answer:

(a) The mean and the standard deviation for the numbers of peas with green pods in the groups of 36 is 27 and 2.6 respectively.

(b) The significantly low values are those which are less than or equal to 21.8. And on the other hand, the significantly higher values are those which are greater than or equal to 32.2.

(c) The result of 15 peas with green pods is a result that is significantly​ low value.

Step-by-step explanation:

We are given 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 36.

The above situation can be represented as a binomial distribution;

where, n = sample of offspring peas = 36

            p = probability that a pea has green pods = 0.75

(a) The mean of the binomial distribution is given by the product of sample size (n) and the probability (p), that is;

                    Mean, $\mu$  =  n $\times$ p

                                    =  36 $\times$ 0.75 = 27 peas

So, the mean number of peas with green pods in the groups of 36 is 27.

Similarly, the standard deviation of the binomial distribution is given by the formula;

            Standard deviation, $\sigma$  =  $\sqrt{n \times p \times (1-p)}$

                                                  =  $\sqrt{36 \times 0.75 \times (1-0.75)}$

                                                  =  $\sqrt{6.75}$  =  2.6 peas

So, the standard deviation for the numbers of peas with green pods in the groups of 36 is 2.6.

             

(b) Now, the range rule of thumb states that the usual range of values lies within the 2 standard deviations of the mean, that means;

          $\mu - 2 \sigma$  =  27 - (2 $\times$ 2.6)

                       =  27 - 5.2 = 21.8

          $\mu + 2 \sigma$  =  27 + (2 $\times$ 2.6)

                       =  27 + 5.2 = 32.2

This means that the significantly low values are those which are less than or equal to 21.8.

And on the other hand, the significantly higher values are those which are greater than or equal to 32.2.

(c) The result of 15 peas with green pods is a result that is a significantly​ low value because the value of 15 is less than 21.8 which is represented as a significantly low value.