Westonci.ca is the premier destination for reliable answers to your questions, brought to you by a community of experts. Experience the convenience of finding accurate answers to your questions from knowledgeable professionals on our platform. Get immediate and reliable solutions to your questions from a community of experienced professionals on our platform.
Sagot :
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.
------------
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.
-----------
Item a:
[tex]43.5 - 3(2.77) = 35.26[/tex]
[tex]43.5 + 3(2.77) = 51.88[/tex]
Within 3 standard deviations of the mean, thus, approximately 99.7%.
-----------
Item b:
[tex]43.5 - 2(2.77) = 38.03[/tex]
[tex]43.5 + 2(2.77) = 49.11[/tex]
Within 2 standard deviations of the mean, thus, approximately 95%.
-----------
Item c:
- 68% is within 1 standard deviation of the mean, so:
[tex]43.5 - 2.77 = 40.73[/tex]
[tex]43.5 + 2.77 = 46.27[/tex]
Approximately 68% of the amounts fall between $40.73 and $46.27.
A similar problem is given at https://brainly.com/question/15967965
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 [tex]\bold{68\%}[/tex] of the measures are within 1 standard deviation of the mean.
- About [tex]\bold{95\%}[/tex] of the measurements are within 2 standard deviations.
- About [tex]\bold{99.7\%}[/tex] of the measures are subject to 3 standard deviations.
Point a:
[tex]\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}[/tex]
Therefore, approximately [tex]\bold{99.7\%}[/tex] within 3 standard deviations from the mean.
Point b:
[tex]\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}\\\\[/tex]
Therefore, approximately [tex]\bold{95\%}[/tex] in 2 standard deviations from the mean.
Point c:
In 1 standard deviation of the mean, [tex]\bold{68\%}[/tex]is as follows:
[tex]\to \bold{43.5-2.77= 40.73}\\\\\to \bold{43.5+2.77= 46.27}[/tex]
About [tex]\bold{68\%}[/tex] of the sums decrease from [tex]\bold{\$40.73 \ and \ \$46.27}[/tex].
So, the final answer are:
- The amount between [tex]\bold{\$35.26 \ and\ \$51.88}[/tex] makes up approximately [tex]\bold{99.7\%}[/tex] of the amounts.
- The amount among [tex]\bold{\$ 38.03\ and\ \$49.11}[/tex] bills amounts to approximately [tex]\bold{95\%}.[/tex]
- About [tex]\bold{68\%}[/tex] of the amounts are [tex]\bold{\$40.73 \ and \ \$46.27}[/tex].
Learn more:
brainly.com/question/14599976
Thanks for using our platform. We're always here to provide accurate and up-to-date answers to all your queries. We appreciate your visit. Our platform is always here to offer accurate and reliable answers. Return anytime. Keep exploring Westonci.ca for more insightful answers to your questions. We're here to help.
