The amount of television viewed by today's youth is of primary concern to Parents Against Watching Television (PAWT). 300 parents of elementary school-aged children were asked to estimate the number of hours per week that their child watches television. The mean and the standard deviation for their responses were 12 and 2, respectively. PAWT constructed a stem-and-leaf display for the data that showed that the distribution of times was a symmetric, mound-shaped distribution. Give an interval where you believe approximately 95% of the television viewing times fell in the distribution.Group of answer choicesless than 16less than 10 and more than 14 hours per weekbetween 8 and 16 hours per weekbetween 6 and 18 hours per week
Question
The amount of television viewed by today's youth is of primary concern to Parents Against Watching Television (PAWT). 300 parents of elementary school-aged children were asked to estimate the number of hours per week that their child watches television. The mean and the standard deviation for their responses were 12 and 2, respectively. PAWT constructed a stem-and-leaf display for the data that showed that the distribution of times was a symmetric, mound-shaped distribution. Give an interval where you believe approximately 95% of the television viewing times fell in the distribution.Group of answer choicesless than 16less than 10 and more than 14 hours per weekbetween 8 and 16 hours per weekbetween 6 and 18 hours per week
Solution
The interval where approximately 95% of the television viewing times fell in the distribution would be between 8 and 16 hours per week. This is because, in a symmetric, mound-shaped distribution (which is a characteristic of a normal distribution), approximately 95% of the data falls within 2 standard deviations of the mean. Given that the mean is 12 and the standard deviation is 2, two standard deviations below the mean is 8 (12 - 22) and two standard deviations above the mean is 16 (12 + 22). Therefore, the interval is between 8 and 16 hours per week.
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