Suppose according to one of Mendel's hybridization experiments, when peas with green pods were crossed with peas with yellow pods, 45% of the offspring pods should be yellow. What is the probability that at least 267 of 570 offspring peas would have yellow pods? Round your answer to four decimal places.
A)0.2005
B)0.4812
C)0.3436
D)0.7995
E)0.3840

Question

Suppose according to one of Mendel's hybridization experiments, when peas with green pods were crossed with peas with yellow pods, 45% of the offspring pods should be yellow. What is the probability that at least 267 of 570 offspring peas would have yellow pods? Round your answer to four decimal places. ​
A)0.2005
B)0.4812
C)0.3436
D)0.7995
E)0.3840

Quizplus · Accepted Answer

The probability of getting at least 267 yellow pods out of 570 offspring peas is the complement of the probability of getting less than 267 yellow pods. The probability of getting less than 267 yellow pods is the sum of the probabilities of getting 0, 1, ..., 266 yellow pods. We can use the binomial distribution to calculate these probabilities. The probability of getting k yellow pods out of n offspring peas is given by:```P(k) = (n choose k) * p^k * (1-p)^(n-k)```where:* n is the number of offspring peas* k is the number of yellow pods* p is the probability of getting a yellow podIn this case, n = 570, k = 267, and p = 0.45. Using the binomial distribution, we can calculate the probability of getting less than 267 yellow pods as:```P(k < 267) = sum(P(k) for k = 0 to 266)```Using a calculator, we find that P(k < 267) = 0.2005. Therefore, the probability of getting at least 267 yellow pods is 1 - P(k < 267) = 1 - 0.2005 = 0.7995.

Suppose According to One of Mendel's Hybridization Experiments, When Peas