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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   We are...

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 We...

Let M=male lizard ages, F=female lizard ages, ρ = correlation, Cov(m,f) = covariance   M = .75F ρ=Cov(M,F)/(σMσF) 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) σM=.75σF   Var(F) = σF2 ρ = 0.75σF2 /...

Sample correlation is calculated this way. numerator: ∑(xi-xbar)(yi-ybar) denominator: squareroot(∑(xi-xbar)2∑(yi-ybar)2)   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. http://en.wikipedia.org/wiki/68%E2%80%9395%E2%80%9399.7_rule   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 25%...

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 0...

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 β :...

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...

Here is a link to an article that points out a bug in Wolfram Alpha related to a comic on xkcd. http://www.explainxkcd.com/wiki/index.php/1292:_Pi_vs._Tau

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   We have 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...

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.   Outcome Probability 2             0.25   (tails, tails) 3    ...

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   Multiplying...

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,...

First notation: 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  14,313*k^11=3000 k^11=3000/14,313 ln(k^11)=ln(3000/14,313)=-1...

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...