Question

Parents Against Watching Television.A society called Parents Against Watching Television (PAWT) is primarily concerned with the amount of television viewed by today’s youth. It asked 300 parents of elementary school aged children to estimate the number of hours their child spent watching television in any given week. The mean and the standard deviation for their responses were 17 and 3, respectively. PAWT then constructed a stem-and-leaf display for the data, which showed that the distribution of the number of hours was a symmetric, mound-shaped distribution. Identify the interval where you believe approximately 95% of the television viewing times fell in the distribution.

Short answer

11 to 23 hours is the interval where 95% of viewing time falls.

Step-by-step solution

Identifying the interval where approx. 95% of television viewing time fell

We have the mean and standard deviation as 17 and 3, respectively.

According to the Empirical Rule, 95% of measurements fall between the 2 standard deviation from mean. Therefore, we have the value of k.

Now we will use the values of mean, s and k to find the intervals.

$$\begin{gathered} \overline{x}\pm 2s \\ Upperrange=\overline{x}+2s \\ =17+2\left(3\right) \\ =17+6 \\ =23 \\ Lowerrange=\overline{x}-2s \\ =17-2\left(3\right) \\ =17-6 \\ =11 \end{gathered}$$

Therefore, 95% of the television viewing time falls between 11 to 23 hours.