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4 years ago

Does adding values that are much greater or much less than the other values in a set of data affect the median of the set

1 answer:

4 0

Well, first off, after you've arranged the entire set numerically, the median is the middle number. Therefore, depending on the numbers in the set, adding another number has the possibility of changing the median. However, it does not matter if the additional values are much greater or much less than the other values.

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tp he Pew Research Center and Smithsonian magazine recently quizzed a random sample of 1006 U.S. adults on their knowledge of sc

alukav5142 [94]

Answer:

This interval (0.175, 0.225) represents the range of values that the true proportion of U.S. adults that can answer the question of 'which gas makes up the most of the atmosphere?' correctly, can take on, with a confidence level of 95%.

Step-by-step explanation:

Confidence Interval is an interval obtaimed from sample data, for the population proportion. It is an interval of range of values where the true population proportion can be found with a certain level of confidence.

Mathematically,

Confidence Interval = (Sample proportion) ± (Margin of error)

Margin of Error is the width of the confidence interval about the mean (sample proportion).

It is given mathematically as,

Margin of Error = (Critical value) × (standard Error of the sample proportion)

Critical value is obtained from the z-tables or the t-tables depending on which information is available. For distributions where information on the population standard deviation is known or it isn't know but the sample size is large enough for the sample standard deviation can approximate the population standard deviation, the z-tables is used and for those distributions whose population standard deviation information is not known, and sample size isn't large enough, the critical value is read off the t-tables.

The critical value depends on the confidence level for both the z-tables and the t-tables critical value.

The interval obtained now represents the region of values where the true population proportion can exist within, at a certain level.of confidence.

Hope this Helps!!!

7 0

3 years ago

In the following problem, check that it is appropriate to use the normal approximation to the binomial. Then use the normal dist

frosja888 [35]

Answer:

a) 0.9920 = 99.20% probability that 15 or more will live beyond their 90th birthday

b) 0.2946 = 29.46% probability that 30 or more will live beyond their 90th birthday

c) 0.6273 = 62.73% probability that between 25 and 35 will live beyond their 90th birthday

d) 0.0034 = 0.34% probability that more than 40 will live beyond their 90th birthday

Step-by-step explanation:

We solve this question using the normal approximation to the binomial distribution.

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 distributions 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:

Sample of 723, 3.7% will live past their 90th birthday.

This means that $n = 723, p = 0.037$ .

So for the approximation, we will have:

$\mu = E(X) = np = 723*0.037 = 26.751$

$\sigma = \sqrt{V(X)} = \sqrt{np(1-p)} = \sqrt{723*0.037*0.963} = 5.08$

(a) 15 or more will live beyond their 90th birthday

This is, using continuity correction, $P(X \geq 15 - 0.5) = P(X \geq 14.5)$ , which is 1 subtracted by the pvalue of Z when X = 14.5. So

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

$Z = \frac{14.5 - 26.751}{5.08}$

$Z = -2.41$

$Z = -2.41$ has a pvalue of 0.0080

1 - 0.0080 = 0.9920

0.9920 = 99.20% probability that 15 or more will live beyond their 90th birthday

(b) 30 or more will live beyond their 90th birthday

This is, using continuity correction, $P(X \geq 30 - 0.5) = P(X \geq 29.5)$ , which is 1 subtracted by the pvalue of Z when X = 29.5. So

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

$Z = \frac{29.5 - 26.751}{5.08}$

$Z = 0.54$

$Z = 0.54$ has a pvalue of 0.7054

1 - 0.7054 = 0.2946

0.2946 = 29.46% probability that 30 or more will live beyond their 90th birthday

(c) between 25 and 35 will live beyond their 90th birthday

This is, using continuity correction, $P(25 - 0.5 \leq X \leq 35 + 0.5) = P(X 24.5 \leq X \leq 35.5)$ , which is the pvalue of Z when X = 35.5 subtracted by the pvalue of Z when X = 24.5. So

X = 35.5

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

$Z = \frac{35.5 - 26.751}{5.08}$

$Z = 1.72$

$Z = 1.72$ has a pvalue of 0.9573

X = 24.5

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

$Z = \frac{24.5 - 26.751}{5.08}$

$Z = -0.44$

$Z = -0.44$ has a pvalue of 0.3300

0.9573 - 0.3300 = 0.6273

0.6273 = 62.73% probability that between 25 and 35 will live beyond their 90th birthday.

(d) more than 40 will live beyond their 90th birthday

This is, using continuity correction, P(X > 40+0.5) = P(X > 40.5), which is 1 subtracted by the pvalue of Z when X = 40.5. So

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

$Z = \frac{40.5 - 26.751}{5.08}$

$Z = 2.71$

$Z = 2.71$ has a pvalue of 0.9966

1 - 0.9966 = 0.0034

0.0034 = 0.34% probability that more than 40 will live beyond their 90th birthday

6 0

3 years ago

Which equation is true when the value of x is 3.5 help

Anestetic [448]

Answer:2x-8=1

Step-by-step explanation:

5 0

3 years ago

Read 2 more answers

Find the slope of the line that passes through (93, -6) and (11, 24).

Lesechka [4]

Answer:

-15/41

Step-by-step explanation:

8 0

3 years ago

Read 2 more answers

Solve by elimination: x-2y= -7 ; 4x+2y= 22

svp [43]

Apply the elimination method to the 2y terms since they are opposites & therefore can eliminate. Combine the rest of the terms, vertically.

x-2y= -7
4x+2y= 22
5x = 15
Divide both sides by 5.
x=3

Plug the x value to one of the original equations and solve for y.

4x + 2y = 22
4(3) + 2y = 22
12 + 2y = 22
Subtract by 12 on both sides.
2y = 10
Divide by 2 on both sides.
y = 5

Therefore, the solution to the system of equations shown is:

x=3 y=5

or

as an ordered pair (3, 5).

6 0

4 years ago