Question

Suppose 17% of the listeners of a radio station listen to it while they work. What is the approximate standard deviation of the proportion for the samples of size 91?
•3.9%
•7.8%
•0.4%
•1.8%

Answer 1

Answer:

The correct answer is 3.9%

Step-by-step explanation:

P : the probability of listening at work, is 17%  or 0.17

Q : the probability of NOT listening at work, is 1 - 0.17, or 83% or 0.83

N : the sample size, is 91

The standard deviation of samples then is

$=\sqrt{\frac{P\times Q}{N}} \\\\=\sqrt{\frac{0.17\times 0.83}{91}}\approx 0.0394\\\\\implies \text{Approximate standard deviation percentage = }\text{standard deviation}\times\text{100}\\=0.00394\times 100\\=3.9\%$

 So, the correct Option is A. 3.9%