Question

Goofy's fast food center wishes to estimate the proportion of people in its city that will purchase its products. Suppose the true proportion is 0.04. If 238 are sampled, what is the probability that the sample proportion will differ from the population proportion by less than 0.037 Round your answer to four decimal places. Tables Keypad Answer/How to Enter) 2 Points prev e here to search

Answer 1

Solution

Given that,

p = 0.04

1 - p = 1 - 0.04 = 0.96

n = 238

$\mu$
_р
= p = 0.04

$\sigma$
_р
=  $\sqrt$[p ( 1 - p ) / n] = $\sqrt$ [(0.04 * 0.96) / 238 ] = 0.0127

$\mu$
_р
  ± 0.03

=P ( 0.01 < < 0.07)

р

= P[(0.01 - 0.04) / 0.0127 < (
р
- $\mu$
_р
) / $\sigma$
_р
< (0.07 - 0.04) / 0.0127 ]

= P(-2.36 < z < 2.36)

= P(z < 2.36) - P(z < -2.36)

Using z table,   

= 0.9909 - 0.0091

= 0.9818