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2 years ago

Which pair of variables shows a clear causal link?

Mathematics

2 answers:

xxTIMURxx [149]2 years ago

8 0

The number of lights switched on in a room and the room's brightness.

LekaFEV [45]2 years ago

4 0

Answer:

The pair of variables that show a clear causal link are the number of lights switched on in a room and the room's brightness

Step-by-step explanation:

Clear casual link indicates two variables that have a completly and unequivocal relation, meaning that changes in one variable produce automatically and with no doubt a change in the other.

Case A does not have this link as these two variables have no relation at all. A person from certian state may have any type of academic degree.

Case B Cost of aviation fuel may be explained by other variables like international prices and flight duration may be explained also due to climate.

Case D- a person may have a pet even under low income levels.

Case C is the only adequate relation, as turning lights on will always increase room's brightness.

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Suppose that 20% of the adult women in the United States dye or highlight their hair. We would like to know the probability that

Rasek [7]

Answer:

71.08% probability that pˆ takes a value between 0.17 and 0.23.

Step-by-step explanation:

We use the binomial approxiation to the normal to solve this question.

Binomial probability distribution

Probability of exactly x sucesses on n repeated trials, with p probability.

Can be approximated to a normal distribution, using the expected value and the standard deviation.

The expected value of the binomial distribution is:

$E(X) = np$

The standard deviation of the binomial distribution is:

$\sqrt{V(X)} = \sqrt{np(1-p)}$

Normal probability distribution

Problems of normally distributed samples can be solved using the z-score formula.

In a set with mean $\mu$ and standard deviation $\sigma$ , the zscore of a measure X is given by:

$Z = \frac{X - \mu}{\sigma}$

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.

When we are approximating a binomial distribution to a normal one, we have that $\mu = E(X)$ , $\sigma = \sqrt{V(X)}$ .

In this problem, we have that:

$p = 0.2, n = 200$ . So

$\mu = E(X) = np = 200*0.2 = 40$

$\sigma = \sqrt{V(X)} = \sqrt{np(1-p)} = \sqrt{200*0.2*0.8} = 5.66$

In other words, find probability that pˆ takes a value between 0.17 and 0.23.

This probability is the pvalue of Z when X = 200*0.23 = 46 subtracted by the pvalue of Z when X = 200*0.17 = 34. So

X = 46

$Z = \frac{X - \mu}{\sigma}$

$Z = \frac{46 - 40}{5.66}$

$Z = 1.06$

$Z = 1.06$ has a pvalue of 0.8554

X = 34

$Z = \frac{X - \mu}{\sigma}$

$Z = \frac{34 - 40}{5.66}$

$Z = -1.06$

$Z = -1.06$ has a pvalue of 0.1446

0.8554 - 0.1446 = 0.7108

71.08% probability that pˆ takes a value between 0.17 and 0.23.

6 0

2 years ago

A group pre-orders 9 tickets for a sightseeing tour, even though they don't have the money to pay for them yet. Each ticket cost

MissTica

9x$32 + 15 is the total debt.
which would be $303.

3 0

2 years ago

Read 2 more answers

A polling agency reported that 66 percent of adults living in the United States were satisfied with their health care plans. The

Tpy6a [65]

Answer:

A) The probability is 0.95 that the percent of adults living in the United States who are satisfied with their health care plans is between 63.6% and 68.4%.

Step-by-step explanation:

A polling agency reported that 66 percent of adults living in the United States were satisfied with their health care plans. The estimate was taken from a random sample of 1,542 adults living in the United States, and the 95 percent confidence interval for the population proportion was calculated as (0.636, 0.684).

This means that we are 95% sure that the true proportion of adults living in the United States who were satisfied with their health care plans is between 0.636 and 0.684.

So the correct answer is:

A) The probability is 0.95 that the percent of adults living in the United States who are satisfied with their health care plans is between 63.6% and 68.4%.

7 0

1 year ago

Juliette spends $6.12 at the store. Morgan spends 3 times as much ad Juliette. Jonah soends $4.29 more than Morgan. How much mon

sladkih [1.3K]

$22.65 is the answer to your question

5 0

1 year ago

Read 2 more answers

Sophia was selling tickets at the high school dance. At the end of the evening, she picked up the cash box and noticed a $5 bill

borishaifa [10]

The first thing we will do in this case is to define variables:
x = number of individual tickets.
y = number of tickets per couple.
We have then that the system of equations that represents the problem is:
10x + 15y = 590
x + 2y = 68
Solving the system we have:
x = 32
y = 18
Substituting we have:
10 (32) + 15 (18) = 590
320 + 270 = 590
590 = 590
Equality is met, therefore the $ 5 bill belongs to the box.
Answer:
the $ 5 bill belong inside the cash box

4 0

2 years ago