Answer:
is is test question and I will solve it for you
Answer: D) 0.438 < p < 0.505
Step-by-step explanation:
We know that the confidence interval for population proportion is given by :-
![\hat{p}\pm z^*\sqrt{\dfrac{\hat{p}(1-\hat{p})}{n}}](https://tex.z-dn.net/?f=%5Chat%7Bp%7D%5Cpm%20z%5E%2A%5Csqrt%7B%5Cdfrac%7B%5Chat%7Bp%7D%281-%5Chat%7Bp%7D%29%7D%7Bn%7D%7D)
, where n= sample size
= Sample proportion.
z* = critical value.
Given : A survey of 865 voters in one state reveals that 408 favor approval of an issue before the legislature.
i.e. n= 865
![\hat{p}=\dfrac{408}{865}\approx0.4717](https://tex.z-dn.net/?f=%5Chat%7Bp%7D%3D%5Cdfrac%7B408%7D%7B865%7D%5Capprox0.4717)
Two-tailed critical avlue for 95% confidence interval : z* = 1.96
Then, the 95 % confidence interval for the true proportion of all voters in the state who favor approval will be :-
![0.4717\pm (1.96)\sqrt{\dfrac{0.4717(1-0.4717)}{865}}\\\\\approx0.4717\pm 0.03327\\\\=(0.4717-0.03327,\ 0.4717+0.03327)=(0.43843,\ 0.50497)\approx(0.438,\ 0.505)](https://tex.z-dn.net/?f=0.4717%5Cpm%20%281.96%29%5Csqrt%7B%5Cdfrac%7B0.4717%281-0.4717%29%7D%7B865%7D%7D%5C%5C%5C%5C%5Capprox0.4717%5Cpm%200.03327%5C%5C%5C%5C%3D%280.4717-0.03327%2C%5C%200.4717%2B0.03327%29%3D%280.43843%2C%5C%200.50497%29%5Capprox%280.438%2C%5C%200.505%29)
Thus, the required 95% confidence interval : (0.438, 0.505)
Hence, the correct answer is D) 0.438 < p < 0.505
I think is the second choice!!!
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The domain of a step function is all real numbers.
Let the number of minutes be = x.
Cost per minute = 18 cents = 0.18
Amount for last call = $20 - $12.08 = $7.92
Number of minutes = Amount / Cost per minute
= 7.92 / 0.18
= 44
Call lasted 44 minutes.