24 Each member of a larger genetics class grows 12 pea plant

24. Each member of a larger genetics class grows 12 pea plants from an independent pea family. Each family is expected to have ¾ plants with smooth peas and ¼ plants with wrinkled peas.

            a. On average, how many winkled pea plants will a student see in her 12

            plants?

            b. What is the stand deviation of the proportion of wrinkled pea plants per

            student?

            c. What is the variance of the proportion of wrinkled pea plants per

            student?

d. Predict what proportion of the students saw exactly two wrinkled pea plants in their sample.

Solution

a)

She should expect 1/4(12) = 3 wrinkled plants. [answer]

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b)

sp = sqrt [p (1 - p)/n] = sqrt [(1/4)(1 - 1/4) / 12]

sp = 0.125 [answer]

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c)

variance = (sp)^2 = 0.015625 [answer]

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d)

Note that the probability of x successes out of n trials is          
          
P(n, x) = nCx p^x (1 - p)^(n - x)          
          
where          
          
n = number of trials =    12      
p = the probability of a success =    0.25      
x = the number of successes =    2      
          
Thus, the probability is          
          
P (    2   ) =    0.232293248 [ANSWER]