Question

From previous polls, it is believed that 66% of likely voters prefer the incumbent. A new poll of 500 likely voters will be conducted. In the new poll, if the proportion favoring the incumbent has not changed, what is the mean and standard deviation of the number preferring the incumbent?(a)mean = 330, standard deviation = 10.59(b)mean = 0.66, standard deviation = 10.59(c)mean = 330, standard deviation = 18.17

Answer 1

Answer:

The mean and standard deviation of the number preferring the incumbent is mean = 330, standard deviation = 10.59.

Step-by-step explanation:

We are given that From previous polls, it is believed that 66% of likely voters prefer the incumbent.

A new poll of 500 likely voters will be conducted. In the new poll the proportion favoring the incumbent has not changed.

Let p = probability of voters preferring the incumbent = 66%

n = number of voters polled = 500

So, the mean of the number preferring the incumbent is given by;

         Mean = $n \times p$ = $500 \times 0.66$

                                = 330 voters

And, standard deviation of the number preferring the incumbent is given by;

          Variance =  $n \times p\times (1-p)$  

                          =  $500 \times 0.66 \times (1-0.66)$

                          =  112.2

So, Standard deviation =  $\sqrt{Variance}$

                                       = $\sqrt{112.2}$  = 10.59