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Ad libitum [116K]
3 years ago
12

A researcher wants to estimate the mean age of all Business Week readers at a 99% confidence level. The standard deviation of ag

es of all Business Week readors is nine years. The sample size that will yield a maximum error of estimate within three years of the population mean is at least:
A. 60
B. 97
C. 185
D. 8
Mathematics
1 answer:
Natasha2012 [34]3 years ago
5 0

Answer:

A. 60

Step-by-step explanation:

We have that to find our \alpha level, that is the subtraction of 1 by the confidence interval divided by 2. So:

\alpha = \frac{1-0.99}{2} = 0.005

Now, we have to find z in the Ztable as such z has a pvalue of 1-\alpha.

So it is z with a pvalue of 1-0.005 = 0.995, so z = 2.575

Now, find the margin of error M as such

M = z*\frac{\sigma}{\sqrt{n}}

In which \sigma is the standard deviation of the population and n is the size of the sample.

We have to find:

n when M = 3, \sigma = 9. So

M = z*\frac{\sigma}{\sqrt{n}}

3 = 2.575*\frac{9}{\sqrt{n}}

3\sqrt{n} = 9*2.575

Dividing both sides by 3

\sqrt{n} = 3*2.575

(\sqrt{n})^{2} = (3*2.575)^{2}

n = 59.68

We round up, so the correct answer is:

A. 60

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C
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<h3>How to find arc angle?</h3>

If two secant intersect in the exterior of a circle, then the measure of the angle formed is half the positive difference of the arcs intercepted.

Therefore, the secants intersect outside the circle at point E.

The arc angle AC can be found as follows:

Therefore,

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