Question

When a scientist conducted a genetics experiments with​ peas, one sample of offspring consisted of

925

​peas, with

701

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

693.75

​(or about

694)

of the peas would have red​ flowers, so the result of

701

peas with red flowers is more than expected.

a. If the​ scientist's assumed probability is​ correct, find the probability of getting

701

or more peas with red flowers.

b. Is

701

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?

If the​ scientist's assumed probability is​ correct, the probability of getting

701

or more peas with red flowers is _____

Answer 1

here mean of distribution=μ=np=		693.75
and standard deviation σ=sqrt(np(1-p))=		13.17
for normal distribution z score =(X-μ)/σx

therefore from normal approximation of binomial distribution and continuity correction:

a)

e probability of getting 701 or more peas with red flowers:

probability =P(X>700.5)=P(Z>(700.5-693.75)/13.17)=P(Z>0.51)=1-P(Z<0.51)=1-0.695=0.3050

b)

No since probability of getting this or more is not less than 0.05

c)

If the​ scientist's assumed probability is​ correct, the probability of getting 701 or more peas with red flowers is 0.3050