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

Answer 1

According to the given 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.  

Therefore

p = 0.04

If 323 are sampled so,

323

Therefore the probability that the sample proportion will differ from the population proportion by greater than 0.03

0.03 | > | P (p-pl > 0.03)-P p(1-p 7n 7n

  

0.03 0.04x (1-0.04) 323

> P (Z| > 2.752)

  $\Rightarrow1- P\left ( \left |Z \right |<2.752\right )$

  

1-P (-2.752 < Z < 2.752)

1-0.9941

  $\Rightarrow 0.0060$

(Round to four decimal places)

Therefore the probability that the sample proportion will differ from the population proportion by greater than 0.03 is
0.0060
.

The area under the standard normal curve which is red shaded are the required area determined as:

0.9941 -1 2 Z-2.752 --2.752