Question

Suppose that a recent poll found that 43% of adults believe that the overall state of moral values is poor. Complete parts (a) through (c).(a) For 250 randomly selected adults, compute the mean and standard deviation of the random variable X, the number of adults who believe that the overall state of moral values is poor.

Answer 1

6It is given that,

$\begin{gathered} n\text{ = 250} \\ p=\text{ 60\% = 0.6} \\ \\ \end{gathered}$

The mean is calculated as,

$\begin{gathered} Mean\text{ = n }\times p \\ Mean\text{ = 250 }\times\text{ 0.6} \\ Mean\text{ = 150} \end{gathered}$

Standard deviation is calculated as,

$\begin{gathered} Standard\text{ deviation = }\sqrt{np(1-p)} \\ Standard\text{ deviation = }\sqrt{250\times0.60\times(1-0.6)} \\ Standard\text{ deviation = }\sqrt{250\times0.60\times0.4} \end{gathered}$

Simplifying further,

$\begin{gathered} Standard\text{ deviation = }\sqrt{60} \\ Standard\text{ deviation = 7.746} \end{gathered}$

Thus the required answer is,

$\begin{gathered} Mean\text{ = 150} \\ Standard\text{ deviation = 7.746} \end{gathered}$