Answer:
a)
So then we can conclude that the true proportion of women with cosmetic dermatitis from using eye shadow at 95% of confidence is between (0.0422 and 0.1410)
b) 
So then we can conclude that the true proportion of women with cosmetic dermatitis from using mascara at 95% of confidence is between (0.0628 and 0.1372)
c) For this case we see that both confidence intervals contains the value of 0.12 so then we can't conclude that only one group is referenced at the significance level of 0.05 used.
Step-by-step explanation:
Part a
The estimated proportion of women with cosmetic dermatitis from using eye shadow is given by:

The confidence interval is at 95% of confidence, our significance level would be given by
and
. And the critical value would be given by:
The confidence interval for the proportion is given by the following formula:
Replacing we got:
So then we can conclude that the true proportion of women with cosmetic dermatitis from using eye shadow at 95% of confidence is between (0.0422 and 0.1410)
Part b: A 95% confidence interval for the women with cosmetic dermatitis from using mascara

So then we can conclude that the true proportion of women with cosmetic dermatitis from using mascara at 95% of confidence is between (0.0628 and 0.1372)
Part c: Suppose you are informed that the true proportion with a nickel allergy for one of the two groups (eye shadow or mascara) is .12. Can you determine which group is referenced? Explain.
For this case we see that both confidence intervals contains the value of 0.12 so then we can't conclude that only one group is referenced at the significance level of 0.05 used.
Answer:
112°
Step-by-step explanation:
Given that the diagonals of trapezoid RSTU are congruent, it is an Isosceles Trapezoid.
One of the properties of an Isosceles Trapezoid is that the base angles are equal.
Therefore if the measure of angle S=112°, the measure of Angle U will also be 112°.
Answer:
that means that the letter p in the equation equals to 500
In a large population, 61% of the people are vaccinated, meaning there are 39% who are not. The problem asks for the probability that out of the 4 randomly selected people, at least one of them has been vaccinated. Therefore, we need to add all the possibilities that there could be one, two, three or four randomly selected persons who were vaccinated.
For only one person, we use P(1), same reasoning should hold for other subscripts.
P(1) = (61/100)(39/100)(39/100)(39/100) = 0.03618459
P(2) = (61/100)(61/100)(39/100)(39/100) = 0.05659641
P(3) = (61/100)(61/100)(61/100)(39/100) = 0.08852259
P(4) = (61/100)(61/100)(61/100)(61/100) = 0.13845841
Adding these probabilities, we have 0.319761. Therefore the probability of at least one person has been vaccinated out of 4 persons randomly selected is 0.32 or 32%, rounded off to the nearest hundredths.
c. No. You have a probability of winning, while your friend has a
probability of winning.
Or it’s A