Question

Lunch break: In a recent survey of 655 working Americans ages 25-34, the average weekly amount spent on lunch was $43.5

Answer 1

Using the Empirical Rule, it is found that:

• a) Approximately 99.7% of the amounts are between $35.26 and $51.88.
• b) Approximately 95% of the amounts are between $38.03 and $49.11.
• c) Approximately 68% of the amounts fall between $40.73 and $46.27.

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The Empirical Rule states that, in a bell-shaped distribution:

• Approximately 68% of the measures are within 1 standard deviation of the mean.
• Approximately 95% of the measures are within 2 standard deviations of the mean.
• Approximately 99.7% of the measures are within 3 standard deviations of the mean.

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Item a:

$43.5 - 3(2.77) = 35.26$

$43.5 + 3(2.77) = 51.88$

Within 3 standard deviations of the mean, thus, approximately 99.7%.

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Item b:

$43.5 - 2(2.77) = 38.03$

$43.5 + 2(2.77) = 49.11$

Within 2 standard deviations of the mean, thus, approximately 95%.

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Item c:

• 68% is within 1 standard deviation of the mean, so:

$43.5 - 2.77 = 40.73$

$43.5 + 2.77 = 46.27$

Approximately 68% of the amounts fall between $40.73 and $46.27.

A similar problem is given at brainly.com/question/15967965

Answer 2

It is often used for predicting results in statistics. This rule could be used as an estimate of the consequence of upcoming data to also be collected but also analyzed after determining a confidence interval and before accumulating precise data.

In a clock-shaped distribution, the empirical rule states:

• About $\bold{68\%}$ of the measures are within 1 standard deviation of the mean.
• About $\bold{95\%}$ of the measurements are within 2 standard deviations.
• About $\bold{99.7\%}$ of the measures are subject to 3 standard deviations.

Point a:

$\to \bold{43.5-3(2.77)= 43.5-8.31= 35.26}\\\\\to \bold{43.5+3(2.77)=43.5+8.31= 51.88}$

Therefore, approximately $\bold{99.7\%}$ within 3 standard deviations from the mean.

Point b:

$\to \bold{43.5-2(2.77)= 43.5-5.54= 38.03}\\\\\to \bold{43.5+2(2.77)= 43.5+ 5.54= 49.11}$

Therefore, approximately $\bold{95\%}$ in 2 standard deviations from the mean.

Point c:

In 1 standard deviation of the mean, $\bold{68\%}$is as follows:

$\to \bold{43.5-2.77= 40.73}\\\\\to \bold{43.5+2.77= 46.27}$

About $\bold{68\%}$ of the sums decrease from $\bold{\ 40.73 \ and \ \ 46.27}$.

So, the final answer are:

• The amount between $\bold{\ 35.26 \ and\ \ 51.88}$ makes up approximately $\bold{99.7\%}$ of the amounts.
• The amount among $\bold{\ 38.03\ and\ \ 49.11}$ bills amounts to approximately $\bold{95\%}.$
• About $\bold{68\%}$ of the amounts are $\bold{\ 40.73 \ and \ \ 46.27}$.

Learn more:

brainly.com/question/14599976