Question

The amount of television viewed by​ today's youth is of primary concern to a certain organization. Three hundred parents of elementary​ school-aged children were asked to estimate the number of hours per week that their child watched television. The mean and the standard deviation for their responses were 12 and 2​, respectively. The organization constructed a​ stem-and-leaf display for the data that showed that the distribution of times was a bell shaped distribution. Give an interval around the mean where most​ (approximately 95%) of the television viewing times fell in the distribution.

Answer 1

Between 8 and 16 hours we can say 95%

Explanation:

Given that X= The amount of television viewed by​ today's youth(in number of hours per week the children watched Tv) has mean 12 and std deviation 2.

Sample size = 300

Since the distribution of sizes is given as bell shaped and sample size is sufficiently large we can assume normality of the distribution.

As per normal 95% lie within 2 std deviations on either side from the mean.

Hence the interval around the mean where most​ (approximately 95%) of the television viewing times fell in the distribution

=(Mean±2 std dev)

= 12±4

=(8,16)