Question

When a scientist conducted a genetics experiments with​ peas, one sample of offspring consisted of 905 ​peas, with 686 of them having red flowers. If we​ assume, as the scientist​ did, that under these​ circumstances, there is a 3 divided by 4 probability that a pea will have a red​ flower, we would expect that 678.75 ​(or about 679​) of the peas would have red​ flowers, so the result of 686 peas with red flowers is more than expected. a. If the​ scientist's assumed probability is​ correct, find the probability of getting 686 or more peas with red flowers. b. Is 686 peas with red flowers significantly​ high? c. What do these results suggest about the​ scientist's assumption that 3 divided by 4 of peas will have red​ flowers? a. If the​ scientist's assumed probability is​ correct, the probability of getting 686 or more peas with red flowers is nothing. ​(Round to four decimal places as​ needed.)

Answer 1

a)

p^ = X/n = 686/905 = 0.75801

when p = 0.75

P(p^ > 0.75801)

= P(Z > ( 0.75801 - 0.75)/sqrt(0.75*0.25/905))

= P(Z > 0.5564 )

= 0.289

b)

since 0.289 > 0.05, this is not significantly high

c)

it is true