Question

Suppose that 20% of the residents in a certain state support an increase in the property tax. An opinion poll will randomly sample 400 state residents and will then compute the proportion in the sample that support a property tax increase. How likely is the resulting sample proportion to be within 04 of the true proportion (ie, between 16 and 247 (Hint: Use the sampling distribution of the sample proportion in this case.) it is certain that the resulting sample proportion will be within.04 of the true proportion There is roughly a 99.7 chance that the resulting sample proportion will be within 01 of the true proportion There is roughly a 95 chance that the resulting sample proportion will be within.04 of the true proportion. There is roughly a 6 chance that the resulting sample proportion will be within 04 of the true proportion

Answer 1

probability of the residents of state that support an increase in the property tax =p=0.2

n=400

we have to find P(0.16<P<0.24)

now

P- P(0.16 <P <0.24) = PC- 0.16 - 0.2 0.2+(1-0.2) - 400 Z < 0.24 - 0.2 ) = 0.2*(1-0.2) P(-2 < Z < 2) = P(Z < 2) - P(Z < -2) = 400 0.977 – 0.023 = 0.954

Hence 3rd option is correct