A scientist conducted a hybridization experiment using peas with green pods and

Question

A scientist conducted a hybridization experiment using peas with green pods and yellow pods. He crossed peas in such a way that 25% (or 150) of the 600 offspring peas were expected to have yellow pods. Instead of getting 150 peas with yellow pods, he obtained 154. Assume that the rate of 25% is correct. a. Find the probability that among the 600 offspring peas, exactly 154 have yellow pods. b. Find the probability that among the 600 offspring peas, at least 154 have yellow pods. c. Which result is useful for determining whether the claimed rate of 25% is incorrect? (Part (a) or part (b)?) d. Is there strong evidence to suggest that the rate of 25% is incorrect? a. The probability that exactly 154 have yellow pods is __________. b. The probability that at least 154 have yellow pods is _________. c. (1) ______________ is useful for determining whether the claimed rate is incorrect. d. Is there strong evidence to suggest that the rate of 25% is incorrect? No Yes (1) Part (a) Part (b)

Explanation / Answer

(12)
(a) Probability that exactly 154 peas have yellow pods
P(X=154) = 600C154 * (0.25)^154 * (0.75)^444 = 0.0617

(b)
mean = np = 600*0.25 = 150
std. dev. = sqrt(npq) = sqrt(600*0.25*0.75) = 10.6066
P(X>154) = P(z>(154-150)/10.6066) = 0.377
0.377 is the probability that at least 154 peas have yellow pods.

(c)
Result in part (B) is useful for determining whether the claimed rate of 25% is incorrect.

(d) As 0.377 is greater than usual significance level of 0.05, we fail to reject the hypothesis. This means there is not enough evidence to suggest that the rate of 25% is incorrect.

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