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 408 are sampled, what is the probability that the sample proportion will differ from the population proportion by less than 0.03? Round your answer to four decimal places.

Answer 1

Solution

Given that,

p = 0.05

1 - p = 1 - 0.05 = 0.95

n = 408

= p = 0.05

=  [p ( 1 - p ) / n] = [(0.05 * 0.95) / 408 ] = 0.0108

0.05 -+ 0.03 = 0.02, 0.08

P( 0.02 <   < 0.08 )

= P[( 0.02 - 0.05) / 0.0108 < ( - ) / < ( 0.08 - 0.05 ) / 0.0108 ]

= P( -2.78 < z < 2.78)

= P(z < 2.78 ) - P(z < -2.78 )

Using z table

= 0.9973 - 0.0027

= 0.9946