Isaac sold 58 of his baseball cards at a collectors show. If this represented 14.5% of his total collection, how many baseball c
1 answer:
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Answer:
And rounded up we have that n=1068
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".
The population proportion have the following distribution
Solution to the problem
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 don't have a prior estimation for the proportion so we can use 0.5 as an approximation for this case
And replacing into equation (b) the values from part a we got:
And rounded up we have that n=1068
Distribute 1/2 to <span>(n – 4):
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Subtract (2n + 3):
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Your equation should now look like this:
</span>
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Combine like terms on both sides:
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Subtract 1/2n from both sides:
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Divide both sides by -5/2 to get n by itself:
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The value of n is 2.</span>
</span>
<span>
Subtract (2n + 3):
</span>
<span>
Your equation should now look like this:
</span>
<span>
Combine like terms on both sides:
</span>
<span>
Subtract 1/2n from both sides:
</span>
<span>
Divide both sides by -5/2 to get n by itself:
</span>
<span>
The value of n is 2.</span>