Question

please help, I am on a time crunch! Thank you in advance!!(:

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 0.05. If 316 are sampled what is the probability that the sample proportion will differ from the population proportion by less than 0.047 Round your answer to four decimal places. Sketch the normal curve described in the scenario. Show supporting work. Answer 3 Points Tables Keypad des Learning

Answer 1

Solution:

Given that,

n = 316

$\hat p$ = 0.05

1 - $\hat p$ = 1 - 0.05= 0.95

$\mu$$\hat p$ =  $\hat p$ = 0.05

$\sigma$$\hat p$ = $\sqrt$ $\hat p$ ( 1 - $\hat p$ ) / n

$\sigma$$\hat p$ =  $\sqrt$ 0.05 * 0.95 / 316

= 0.0388

$\sigma$$\hat p$ = 0.0388

Differ Less than 0.04 = 0.05 - 0.01 =0.04 , 0.05 + 0.04 =0.09  

P(  $\hat p$ < 0.04 )

P ( 0.01 < $\hat p$ < 0.09 )

P ( 0.01 - 0.05 / 0.0388 ) < ( $\hat p$ -   $\mu$$\hat p$ / $\sigma$ $\hat p$ ) < ( 0.09 - 0.05 / 0.0388 )

P ( - 0.04 / 0.0388 < z < 0.04 / 0.0388 )

P (-1.03 < z < 1.03 )

P ( z < 1.03 ) - p ( z < -1.03 )

Using z table

= 0.8485 - 0.1515

= 0.6970

Probability = 0.6970