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2 years ago

PLEASE help with these 3 pretty easy problems and explain how you got them!!! I will mark brainliest if right!!!!!!!

Mathematics

1 answer:

Alona [7]2 years ago

8 0

Answer:

Step-by-step explanation:

$\frac{x - 3}{18} = \frac{12}{9}$

$18 \times \frac{x - 3}{18} = 18 \times \frac{12}{9}$

$x−3=9(2)⋅ \frac{12}{9}$

$x−3=2⋅12$

$x−3=24$

$x = 27$

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C. 70

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Brewed decaffeinated coffee contains some caffeine. We want to estimate the amount of caffeine in 8 ounce cups of decaf coffee a

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We would have to take a sample of 62 to achieve this result.

Step-by-step explanation:

Confidence level of 95%.

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

$\alpha = \frac{1 - 0.95}{2} = 0.025$

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That is z with a pvalue of $1 - 0.025 = 0.975$ , so Z = 1.96.

Now, find the margin of error M as such

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Assume that the standard deviation in the amount of caffeine in 8 ounces of decaf coffee is known to be 2 mg.

This means that $\sigma = 2$

If we wanted to estimate the true mean amount of caffeine in 8 ounce cups of decaf coffee to within /- 0.5 mg, how large a sample would we have to take to achieve this result?

We would need a sample of n.

n is found when $M = 0.5$ . So

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

$0.5 = 1.96\frac{2}{\sqrt{n}}$

$0.5\sqrt{n} = 2*1.96$

Dividing both sides by 0.5

$\sqrt{n} = 4*1.96$

$(\sqrt{n})^2 = (4*1.96)^2$

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Rounding up

We would have to take a sample of 62 to achieve this result.

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2 years ago