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dsp73
3 years ago
9

An IQ test is designed so that the mean is 100 and the standard deviation is 12 for the population of normal adults. Find the sa

mple size necessary to estimate the mean IQ score of statistics students such that it can be said with 90​% confidence that the sample mean is within 2 IQ points of the true mean. Assume that sigmaequals12 and determine the required sample size using technology. Then determine if this is a reasonable sample size for a real world calculation. The required sample size is 97. ​(Round up to the nearest​ integer.) Would it be reasonable to sample this number of​ students? Yes. This number of IQ test scores is a fairly large number. Yes. This number of IQ test scores is a fairly small number. No. This number of IQ test scores is a fairly large number. No. This number of IQ test scores is a fairly small number.
Mathematics
1 answer:
Julli [10]3 years ago
5 0

Answer:

Step-by-step explanation:

Given that IQ mean is 100 and std dev = 12 for normal adults

Confidence level =90%\\Z critical value = 1.645\\Margin of error = 2\\Margin of error = 1.645* std error =2\\Std error = 1.216

Std error = \frac{12}{\sqrt{n} } =1.216

n=(\frac{12}{1.216} )^2 =97.38

i.e. sample size should be atleast 97

The required sample size is 97.

This is reasonable as this is greater than 30

Yes. This number of IQ test scores is a fairly large number.

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Hey there!

Your answer is C.

If you take the lengths of the legs of the triangle, which are 12 and 4, we can multiply them by the scale factor to see what the legs of our new triangle is.

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So, the legs of our new triangle have lengths of 1 and 3.

We can see that option C has the correct triangle in red.

If we're looking at the ratio of rise to run of each triangle, it is 1/3 for both the large triangle and the small triangle.

The rise for the larger triangle is 4, and the run is 12. That is 4/12, which can be simplified to 1/3.

The rise for the smaller triangle is 1, and the run is 3. That is 1/3, which is all the way simplified already.

These triangles are similar because the first one was dilated to get the second one, which explains why the ratios are the same.

Hope this helps!  

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