7/8 of a rectangle is colored red. Damien cuts this red part into a number of pieces so that each piece is 1/24 of the whole rec
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The total monthly bill of the gym = $53
The cost of membership of a month = $25
Let 'n' be extra the number of hours Bella worked on.
The cost for working on extra hours = $4
So, we have to determine the equation, Bella worked out after hours.
We will determine the equation by:
(Monthly cost of membership) + ( cost for extra hours number of hours extra worked on ) = Total monthly bill received
So, we get
$25+4n = $53 is the required equation.
Therefore, $25+4n = $53 equation can be used to determine how many times Bella worked out after hours.
Answer:
1) n=48
2) n=298
3) n=426
Step-by-step explanation:
Previous concepts
A confidence interval is "a range of values that’s likely to include a population value with a certain degree of confidence. It is often expressed a % whereby a population means lies between an upper and lower interval".
The margin of error is the range of values below and above the sample statistic in a confidence interval.
Normal distribution, is a "probability distribution that is symmetric about the mean, showing that data near the mean are more frequent in occurrence than data far from the mean".
represent the real population proportion of interest
represent the estimated proportion for the sample
n is the sample size required (variable of interest)
represent the critical value for the margin of error
The population proportion have the following distribution
Part 1
In order to find the critical value we need to take in count that we are finding the interval for a proportion, so on this case we need to use the z distribution. Since our interval is at 90% of confidence, our significance level would be given by and
. And the critical value would be given by:
The margin of error for the proportion interval is given by this formula:
(a)
And on this case we have that and we are interested in order to find the value of n, if we solve n from equation (a) we got:
(b)
We can assume that the estimated proportion is 0.23 for the 25 to 30 group. And replacing into equation (b) the values from part a we got:
And rounded up we have that n=48
Part 2
The margin of error on this case changes to 0.04 so if we use the same formula but changing the value for ME we got:
And rounded up we have that n=298
Part 3
In order to find the critical value we need to take in count that we are finding the interval for a proportion, so on this case we need to use the z distribution. Since our interval is at 95% of confidence, our significance level would be given by and
. And the critical value would be given by:
The margin of error for the proportion interval is given by this formula:
(a)
And on this case we have that and we are interested in order to find the value of n, if we solve n from equation (a) we got:
(b)
We can assume that the estimated proportion is 0.23 for the 25 to 30 group. And replacing into equation (b) the values from part a we got:
And rounded up we have that n=426