There are some problems with how this question is worded, but here is how I interpret it.
Let S be the patient is saved.
Let D be a defibrillator is used.
Let A be a defibrillator is in the area.
The event that a defibrillator is used within 5 minutes is D∩A
What you want is P(X<220)-P(X<170). A lot of technology tools will give you this directly, but if you want to convert the problem in to Z scores to use a table of the standard normal distribution, this is how you do it.
For X = 220 Z=(220-200)/50 = 0.4
For X = 170 Z=(170-200)/50...
For simple linear regression the model is
y = α + βx
In this case, y is the final exam grade and x is the midterm grade.
β=rxy(sy/sx) where rxy is the correlation coefficient, sy is the standard deviation of y, and sx is the standard deviation of x.
α = ybar - β*xbar
Let M=male lizard ages, F=female lizard ages, ρ = correlation, Cov(m,f) = covariance
M = .75F
Cov(m,f) = E[MF] - E[M]E[F] = E[.75F*F] - E[0.75F]*E[F] = 0.75(E[F2]-E[F]2) = 0.75*Var(F)
Var(F) = σF2
ρ = 0.75σF2 /...
Sample correlation is calculated this way.
numerator: (70-69.5)(160-162)+(69-69.5)(164-162) = (0.5)(-2)+(-0.5)(2) = -1+-1=-2
This will mean that the correlation will be negative...
Reference the graphic in this article.
What we have here is a range that is 2 standard deviations below the mean (72.2-2*6.8=58.6) to the mean.
Looking at the graphic we see that the percentage from μ...
This time I will say more about how to set up the Markov matrix.
Let's let the first column be what happens to GTT customers.
75% stay with GTT (g)
5% go to NCJ (n)
20% got to Dash (d)
The second column is what happens to NCJ customers
25% go to g
50% stay with n
This is an example of a Markov chain problem. Let x be the number of preferred drivers, let y be the number of satisfactory drivers, and let z be the number of poor drivers. Then we can set up a matrix and a vector this way.
Matrix A vector u
The CAPM model says that the return on an asset includes the risk free rate of return plus additional return based on the asset's risk relative to the market.
ra : expected rate of return of asset
rf : risk-free rate of return
rm : expected rate of return of market
This can be solved with a system of equations. Let x be the amount invested at 6% and let y be the amount invested at 8%.
You know that the total invested is 10,000. This yields one equation:
x + y = 10,000
You also know that the interest earned on x plus the...
Determine the 2010th term for the following sequence: 1,2,3,6,7,14,15,30,31,62,63
Here is a link to an article that points out a bug in Wolfram Alpha related to a comic on xkcd.
This is an example of exponential growth. The number of cells after n days can be modeled with the function f(n) = 3000*1.07^n
3000*1.07^n = 3630
1.07^n = 1.21
ln(1.07^n) = ln(1.21)
n*ln(1.07) = ln(1.21)
n = ln(1.21)/ln(1.07) ≈ 2.817
The expected value is the sum of the products of all outcomes and the respective probabilities. In your example, the outcomes and the probabilities are listed below.
2 0.25 (tails, tails)
Let x be the amount invested at 6% and y be the amount invested at 10%.
One equation states that the total invested is $12,000
x + y = 12,000
Another equation states that the interest earned is $1040
0.06x + 0.10y = 1040
One possible pattern is that the odd-numbered terms are 7, 8, 9, 10, 11, ... and the even numbered terms are 7*3, 7*3^2, 7*3^3,...
Given this pattern the next term is 189
a) The mode is the grade that occurs most often. 4 occurs 12 times, more than any other grade. 4 is the mode.
b) The median grade is found by ordering all the grades from least to greatest, and then finding the midpoint between the 25th and 26th ordered grade. I will count up the...
The hint to draw a Venn diagram is a good one. Since I can't do that here, I will describe my diagram. It is 3 circles that overlap to create 7 regions: Failed math only, failed physics only, failed chemistry only, failed math and chemistry but not physics, failed math and physics but not chemistry,...
E[X] means the expected value of X and equals the mean of X.
E[X^2] means the expected value of X^2 and can be calculated given the mean and standard deviation of X.
Var(X) = E[X^2] - (E[X])^2 and is equal to the square of the standard deviation of X.
It follows that...
a) linear in this case means a constant decrease in absolute terms. We want the population do decrease 11,313 in 11 years. The rate of change is -11,313/11=-1028.5 swans/year.
b) exponential in this case means constant percentage change. We set up this equation
This is a binomial distribution problem. I highly recommend researching this distribution online or in your textbook. Here is the pmf. P(N=n) = p(n) = k C n q^n*(1-q)^(k-n) where k is the total number of "trials," n is the number of "successes," and q is the probability of success...