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Aleonysh [2.5K]
3 years ago
9

A miniature-doll collector has a total of 254 unique dolls. the collector can afford to add 3 unique dolls a week to the collect

ion. which algebraic expression represents the number of unique pieces the collector has at the end of w weeks?
Mathematics
1 answer:
Olenka [21]3 years ago
4 0
One week = 3 dolls
two weeks = 3 × 2 dolls
three weeks = 3 × 3 dolls
four weeks = 3 × 4 dolls
five weeks = 3 × 5 dolls

'w' weeks = 3 × w dolls
'w' weeks = 3w dolls

Initial number of dolls = 254 dolls

Number of dolls after 'w' weeks = 254 + 3w

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Answer:

Lower = 231.134- 3.098=228.036

Upper = 231.134+ 3.098=234.232

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.

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\bar X represent the sample mean for the sample  

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s represent the sample standard deviation

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Solution to the problem

The confidence interval for the mean is given by the following formula:

\bar X \pm t_{\alpha/2}\frac{s}{\sqrt{n}}   (1)

And for this case we know that the 95% confidence interval is given by:

\bar X=\frac{233.002 +229.266}{2}= 231.134

And the margin of error is given by:

ME = \frac{233.002 -229.266}{2}= 1.868

And the margin of error is given by:

ME= t_{\alpha/2} \frac{s}{\sqrt{n}}

The degrees of freedom are given by:

df = n-1 = 5-1=4

And the critical value for 95% of confidence is t_{\alpha/2}= 2.776

So then we can find the deviation like this:

s = \frac{ME \sqrt{n}}{t_{\alpha/2}}

s = \frac{1.868* \sqrt{5}}{2.776}= 1.506

And for the 99% confidence the critical value is: t_{\alpha/2}= 4.604

And the margin of error would be:

ME = 4.604 *\frac{1.506}{\sqrt{5}}= 3.098

And the interval is given by:

Lower = 231.134- 3.098=228.036

Upper = 231.134+ 3.098=234.232

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Answer:

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