Question

A greenhouse 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. A) Describe the sampling distribution of , the proportion of adults who plant a vegetable garden. B) What is the probability that in a random sample of 1000 customers more than 30% plant a vegetable garden? C) Would it be unusual for a random sample of 1000 customers to result in 250 or fewer plant a garden? Why?

Answer 1

a) For the proportion of adults who plant a vegetable garden, the distribution would be given as:

Therefore it is a normal distribution.

b) The required probability here is computed as:

Converting this to a standard normal variable, we get here:

Getting this from the standard normal tables, we get here:

Therefore 0.0795 is the required probability here.

c) The required probability required here is:

P( X <= 250 )

Converting this to a proportion, we get:

P( p < = 0.25)

Converting this to a standard normal variable, we get:

Getting it from the standard normal tables, we get:

As the given probability is less than 0.05, therefore yes it would be unusual according to the given parameters.