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3 years ago

How to solve this using probability

Mathematics

1 answer:

Fudgin [204]3 years ago

8 0

To solve this using probability simply count the shapes that have at least 4 sides, and represent it as a fraction among all shapes in the spinner.

P(4 sides) = 5/6.
P(tails) = 1/2.

Both are independent events and as such must be multiplied with each other.

5/6 • 1/2 = 5/12,

This is the combined probability of both events occurring.

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The brand manager for a brand of toothpaste must plan a campaign designed to increase brand recognition. He wants to first deter

JulsSmile [24]

Answer:

1) n=114

2) n=59

3) On this case no, because if we survey just the adults of the nearest college that would be a convenience sample. And when we use "convenience sample" we have some problems associated to bias. This methodology it's not appropiate in order to have a good estimation of the parameter of interest. It's better use a random, cluster or stratified sampling.

Step-by-step explanation:

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

$p \sim N(p,\sqrt{\frac{\hat p(1-\hat p)}{n}})$

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 80% of confidence, our significance level would be given by $\alpha=1-0.80=0.2$ and $\alpha/2 =0.1$ . And the critical value would be given by:

$z_{\alpha/2}=-1.28, z_{1-\alpha/2}=1.28$

Part 1

The margin of error for the proportion interval is given by this formula:

$ME=z_{\alpha/2}\sqrt{\frac{\hat p (1-\hat p)}{n}}$ (a)

And on this case we have that $ME =\pm 0.06$ or 6% points, and we are interested in order to find the value of n, if we solve n from equation (a) we got:

$n=\frac{\hat p (1-\hat p)}{(\frac{ME}{z})^2}$ (b)

Since we don't have a prior estimate of $\het p$ we can use 0.5 as a good estimate, replacing into equation (b) the values from part a we got:

$n=\frac{0.5(1-0.5)}{(\frac{0.06}{1.28})^2}=113.77$

And rounded up we have that n=114

Part 2

On this case we have a prior estimate for the population proportion and is $\hat p =0.85$ so replacing the values into equation (b) we got:

$n=\frac{0.85(1-0.85)}{(\frac{0.06}{1.28})^2}=58.027$

And rounded up we have that n=59

Part 3

On this case no, because if we survey just the adults of the nearest college that would be a convenience sample. And when we use "convenience sample" we have some problems associated to bias. This methodology it's not appropiate in order to have a good estimation of the parameter of interest. It's better use a random, cluster or stratified sampling.

5 0

3 years ago

A painter is painting a rectangular wall that measures 20.5 ft by 16.4 ft. Each gallon can of paint covers 200 square feet. What

alekssr [168]

The painter needs at least two gallons of paint to cover the wall.

To get this answer, you first need to find the area of the wall; by multiplying 20.5 x 16.4. This will get you 336.2.

Then, you need to divide 336.2 by 200. This will get you approx. 1.6.

If it's asking for partial gallons as well, stop here. Your answer is 1.6.

If not, continue.

Unless you're including partial gallons, you can't get 1.6 gallons of paint, so you need to round up. This will be 2 gallons.

5 0

2 years ago