Question

you gathered data on how many hours people spent gardening each week in a local neighborhood. the responses from 10 individuals were: \\{12, 14, 16, 15, 13, 17, 16, 15, 14, 13\\}. using this data set that follows a normal distribution, calculate the mean and standard deviation. then, estimate the population percentage within 3 standard deviations of the mean.

use the drop-down arrow to choose the correct value.

the mean of the data set is dropdown

the standard deviation of the data set is dropdown

this means 99.7% of the data falls between dropdown and dropdown

Explanation:

Calculate the sample mean

$$ \bar{x} = \frac{12 + 14 + 16 + 15 + 13 + 17 + 16 + 15 + 14 + 13}{10} = \frac{145}{10} = 14.5 $$

Calculate the sample standard deviation

$$
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$$

Determine the interval for 3 standard deviations

$$
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$$

Answer:

You gathered data on how many hours people spent gardening each week in a local neighborhood. The responses from 10 individuals were: \(\{12, 14, 16, 15, 13, 17, 16, 15, 14, 13\}\). Using this data set that follows a normal distribution, calculate the mean and standard deviation. Then, estimate the population percentage within 3 standard deviations of the mean.

Use the drop-down arrow to choose the correct value.

The mean of the data set is <blank>14.5</blank>

The standard deviation of the data set is <blank>1.58</blank>

This means 99.7% of the data falls between <blank>9.76</blank> and <blank>19.24</blank>