Question

A door delivery florist wishes to estimate the proportion of people in his city that will purchase his flowers. Suppose the true proportion is 0.05. If 355 are sampled, what is the probability that the sample proportion will differ from the population proportion by more than 0.03? Round your answer to four decimal places.

Answer 1

1.0000

Explanation:

Given that a door delivery florist wishes to estimate the proportion of people in his city that will purchase his flowers.

True proportion = 0.05

sample size n = 355

Sample proportion mean= 0.05

Sample proportion std error =
`\sqrt{(pq)/(n) } \\=\sqrt{(0.05*0.95)/(355) } \\=0.0116`

Probability that the sample proportion will differ from the population proportion by more than 0.03

=
`P(|P-p|>0.03)\\= P(|Z|>0.03*0.0116)\\= P(|Z|>0.000348)\\= 0.99999`

i.e. almost certain