Question

refer to the accompanying table, which describes the number of adults in groups of five who reported sleepwalking. find the mean and standard deviation for the numbers of sleepwalkers in groups of five. click the icon to view the data table. the mean is sleepwalker(s). (round to one decimal place as needed.)

Explanation:

Since the data - table is not provided, assume the following general steps for a discrete probability distribution to find the mean $\mu$ and standard deviation $\sigma$.

Let $x$ be the number of sleep - walkers and $P(x)$ be the corresponding probability.

Step1: Calculate the mean $\mu$

The formula for the mean of a discrete probability distribution is $\mu=\sum_{x}x\cdot P(x)$. Multiply each value of $x$ by its probability $P(x)$ and sum these products.
$$\mu=\sum_{x}x\cdot P(x)$$

Step2: Calculate the variance $\sigma^{2}$

The formula for the variance of a discrete probability distribution is $\sigma^{2}=\sum_{x}(x - \mu)^{2}\cdot P(x)$. First, find the difference between each $x$ value and the mean $\mu$, square it, multiply by the probability $P(x)$, and sum these values.
$$\sigma^{2}=\sum_{x}(x - \mu)^{2}\cdot P(x)$$

Step3: Calculate the standard deviation $\sigma$

The standard deviation is the square - root of the variance. So $\sigma=\sqrt{\sigma^{2}}$.
$$\sigma=\sqrt{\sum_{x}(x - \mu)^{2}\cdot P(x)}$$

If we had the actual data in the form of a table with values of $x$ (number of sleep - walkers) and $P(x)$ (probability of having $x$ sleep - walkers), we would substitute the values into the above formulas.

Answer:

Since the data table is not given, we cannot provide numerical answers. But the mean is calculated using $\mu=\sum_{x}x\cdot P(x)$ and the standard deviation is calculated using $\sigma=\sqrt{\sum_{x}(x - \mu)^{2}\cdot P(x)}$ after finding the mean.