Explain why a sample of 30 dentists from a large city taken to estimate the median income of all residents of that large city is
1 answer:
You might be interested in
Answer:
A line passing through the points (-1,-4),(0,0) and (1,4)
Step-by-step explanation:
we know that
A relationship between two variables, x, and y, represent a proportional variation if it can be expressed in the form or
In a proportional relationship the constant of proportionality k is equal to the slope m of the line and the line passes through the origin
<u><em>Verify each case</em></u>
Part 1) A line passing through the points (-4,0) and (0,-2)
This line not represent a direct variation, because the line not passes through the origin.
Part 2) A line passing through the points (-5,4) and (0,3)
This line not represent a direct variation, because the line not passes through the origin.
Part 3) A line passing through the points (-4,-6) and (0,3)
This line not represent a direct variation, because the line not passes through the origin.
Part 4) A line passing through the points (-1,-4),(0,0) and (1,4)
The line passes through the origin
Find out the value of k
For the point (-1,-4)
substitute
For the point (1,4)
substitute
The linear equation is
This line represent a direct variation
Answer:
a) The expected value is
b) The variance is
Step-by-step explanation:
We can assume that both marbles are withdrawn at the same time. We will define the probability as follows
#events of interest/total number of events.
We have 10 marbles in total. The number of different ways in which we can withdrawn 2 marbles out of 10 is .
Consider the case in which we choose two of the same color. That is, out of 5, we pick 2. The different ways of choosing 2 out of 5 is . Since we have 2 colors, we can either choose 2 of them blue or 2 of the red, so the total number of ways of choosing is just the double.
Consider the case in which we choose one of each color. Then, out of 5 we pick 1. So, the total number of ways in which we pick 1 of each color is . So, we define the following probabilities.
Probability of winning:
Probability of losing
Let X be the expected value of the amount you can win. Then,
E(X) = 1.10*probability of winning - 1 probability of losing =
Consider the expected value of the square of the amount you can win, Then
E(X^2) = (1.10^2)*probability of winning + probability of losing =
We will use the following formula
Thus
Var(X) =
Answer:
a) The 95% confidence interval would be given by (509.592;550.308)
b) n=523 rounded up to the nearest integer
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".
represent the sample mean for the sample
population mean
s=70 represent the sample standard deviation
n=48 represent the sample size (variable of interest)
Confidence =95% or 0.995
Part a
The confidence interval for the mean is given by the following formula:
(1)
The degrees of freedom are df=n-1=48-1=47
Since the Confidence is 0.95 or 95%, the value of and
, and we can use excel, a calculator or a table to find the critical value. The excel command would be: "=-T.INV(0.025,47)".And we see that
Now we have everything in order to replace into formula (1):
So on this case the 95% confidence interval would be given by (509.592;550.308)
Part b
The margin of error is given by this formula:
(a)
Assuming that
And on this case we have that ME =6msec, and we are interested in order to find the value of n, if we solve n from equation (a) we got:
(b)
The critical value for 95% of confidence interval is provided, , replacing into formula (b) we got:
So the answer for this case would be n=523 rounded up to the nearest integer