Question

When a scientist conducted a genetics experiments with​ peas, one sample of offspring consisted of 941 ​peas, with 710 of them having red flowers. If we​ assume, as the scientist​ did, that under these​ circumstances, there is a 3 divided by 43/4 probability that a pea will have a red​ flower, we would expect that 705.75 ​(or about 706​) of the peas would have red​ flowers, so the result of 710 peas with red flowers is more than expected.

a. If the​ scientist's assumed probability is​ correct, find the probability of getting 710 or more peas with red flowers.

b. Is 710 peas with red flowers significantly​ high?

c. What do these results suggest about the​ scientist's assumption that 3 divided by 43/4 of peas will have red​ flowers?

Answer 1

Here we have

n=941 , p=3/4

a)

Using normal approximation sampling distribution of sample proportion of red peas will be normal with mean

and standard deviation

The z-score for is

The probability of getting 710 or more peas with red flowers is

b)

No because above probability is not less than 0.05.

c)

Since the result of 710 peas with red flowers is not significantly high, it is not strong evidence against the scientist's assumption that 3/4 of peas will have red flowers.