## Related questions with answers

Advertising researchers have developed a theory that states that commercials that appear in violent television shows are less likely to be remembered and will thus be less effective. After examining samples of viewers who watch violent and nonviolent programs and asking them a series of five questions about the commercials, the researchers produced the following probability distributions of the number of correct answers.

$\boldsymbol{x}$ | 0 | 1 | 2 | 3 | 4 | 5 |
---|---|---|---|---|---|---|

$\boldsymbol{P}(\boldsymbol{x})$ | $.36$ | $.22$ | $.20$ | $.09$ | $.08$ | $.05$ |

$\boldsymbol{x}$ | 0 | 1 | 2 | 3 | 4 | 5 |
---|---|---|---|---|---|---|

$\boldsymbol{P}(\boldsymbol{x})$ | $.15$ | $.18$ | $.23$ | $.26$ | $.10$ | $.08$ |

Calculate the mean and standard deviation of the number of correct answers among viewers of nonviolent television programs.

Solution

VerifiedWe need to find the mean and the standard deviation the number of correct answers among viewers of nonviolent television programs $(X)$.

The mean or the expected value of $X$, denoted by $E(X)$, can be computed as follows:

$\begin{align*} E(X)&=\sum x P(x)\\ &=0\cdot0.15+1\cdot 0.18+2\cdot 0.23+3\cdot 0.26+4\cdot0.10 +5\cdot 0.08\\ &=2.22 \end{align*}$

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