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2 years ago

Find the variance of 101, 102, 100, 100, 110, 109, 109, 108, 109

1 answer:

6 0

101, 102, 100, 100, 110, 109, 109 ,108, 109 average to 105.3

subtracting the mean from each number yields the below-

-4,-3,-5,-5,5,4,4,3,4

Squaring each number gives-

16,9,25,25,16,16,9,16

The average of these numbers is 12.89 to two decimal places, so your variance is 12.89

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A marketing firm wants to estimate how much root beer the average teenager drinks per year. A previous study found a standard de

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Answer:

At least 832 teenargers must be interviewed.

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.

How many teenagers must the firm interview in order to have a margin of error of at most 0.1 liter when constructing a 99% confidence interval

At least n teenargers must be interviewed.

n is found when M = 0.1.

We have that $\sigma = 1.12$

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

$0.1 = 2.575*\frac{1.12}{\sqrt{n}}$

$0.1\sqrt{n} = 2.575*1.12$

$\sqrt{n} = \frac{2.575*1.12}{0.1}$

$(\sqrt{n})^{2} = (\frac{2.575*1.12}{0.1})^{2}$

$n = 831.7$

Rounding up

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2 years ago

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An ostrich can run 6 mph faster than a giraffe. An ostrich can run 7 miles in the same time that a giraffe can run 6 miles. Find

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NOTE THIS IS AN EXAMPLE:

Let t = time, s = ostrich, and g = giraffe.

Here's what we know:

s = g + 5 (an ostrich is 5 mph faster than a giraffe)

st = 7 (in a certain amount of time, an ostrich runs 7 miles)

gt = 6 (in the same time, a giraffe runs 6 miles)

We have a value for s, so plug it into the first equation:

(g + 5)t = 7

gt = 6

Isolate g so that we can plug that variable value into the equation:

g = 6/t

so that gives us:

(6/t + 5)t = 7

Distribute:

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Subtract 6:

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Divide by 5:

t = 1/5 of an hour (or 12 minutes)

Now that we have a value for time, we can plug them into our equations:

1/5 g = 6

multiply by 5:

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s = 30 + 5

s = 35 mph

Check by imputing into the second equation:

st = 7

35 * 1/5 = 7

7 = 7

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2 years ago