Question

Step 1

Let X be the number of red flowers in the sample of offspring of 899 peas.

The total number of spring is 899.

The scientist has assumed that the probability of getting a pea that have red flower is 0.75.

That is the success event is getting a pea that have red flower and failure event is not getting a pea that have red flower.

*The assumptions for binomial distribution:*

- The number of trials is fixed.
- There are two outcomes success and failure with success probability p.
- Each of the trials will be independent.

Here, all the three assumptions are satisfied, therefore it can be said that X follows binomial distribution with n = 899, p = 0.75 (according to scientist’s assumption).

Step 2

The pmf of binomial distribution is,

Step 3

**a.**

Assuming the scientist’s assumed probability is correct, the probabi...

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