Agreenhouse in a? tri-county area has kept track of its customers for the last several years and has determined that? 28% of its customers plant a vegetable garden in the spring. the greenhouse obtains a random sample of 1000 of its customers. what is the mean of the sampling distribution of modifyingabove p with caretp? , the sample proportion of customers that plant a vegetable garden in the? spring?

The mean is 280 customers.

The sample proportion is 28%.

Explanation:

For each customer, there are only two possible outcomes. Either they plant a vegetable in the spring, or they do not. This means that we can solve this problem using concepts of the binomial probability distribution.

Binomial probability distribution.

Probability of exactly x sucesses on n repeated trials, with p probability. Has an expected value of:

In this problem, we have that:

There are 1000 customers, so .

28% of its customers plant a vegetable garden in the spring. This means that .

So:

What is the mean of the sampling distribution of modifyingabove p with caretp?

The mean is the expected value, so:

The mean is 280 customers.

The sample proportion of customers that plant a vegetable garden in the? spring?

It is the same as the population proportion, so the sample proportion is 28%.