How The Response Variable Changes Essay Example

$26,000. Since $27,059 > $26,000, the sales were overestimated. Of the 46 individuals who responded, 25 are concerned, and 21 are not concerned. of those concerned about security are male and 5 of those not concerned are male. If a respondent is selected at random, find each of the fallowing conditional probabilities. The respondent is male, given that the respondent is not concerned about security. P(Male|Not Concerned) = 521 = 0. 238 . The respondent is not concerned about security, given that is female P(Not Concered|Female) = 1632 = 0. 500. The respondent is female, given that the respondent is concerned about security. P(Female|Concerned) = 1625 = 0. 40 14) It was found that 76% of the population were infected with a virus, 21% were without clean water, and 18% were infected and without clean water.

What’s the probability that a surveyed person had clean water and was not infected? 21 had clean water and was not infected. A survey concluded that 54. 4% of the households in a particular country have both a landline and a cell phone, 32. 6% have only cell phone services but no landline, and 4. 6% have no telephone services at all. )

Finally, the standard deviation also known as ? is the square root of the variance.  Var(x) = 0. 69 = 0. 83 Therefore, the standard deviation of the number of nights potential customers will need is approximately 0. 83 nights. 7) A grocery supplier believes that in a dozen eggs, the mean number of broken eggs is 0. 2 with a standard deviation of 0. 1 eggs. You buy 3 dozen eggs without checking

them.

How many broken eggs do you get? The expected value of the sum of random variables is the sum of the expected values of each idividula random variable.  Find the sum of the expected values where X is the total number of broken eggs in the three dozen, and X, X, X Represent the three individual dozen eggs. E(X) = E(X1) + EX2+ EX3 = 0. 2 + 0. 2 + 0. 2 = 0. 6 Therefore, the expected value of X is 0. 6 eggs.

What’s the standard deviation? The variance of the sum of independent variables is the sum of their individual variances. Find the variance for each carton, add the variances, and then take the square root of the sum to find the standard deviation. The variance of each individual dozen is the square of each dozens standard deviation. Var(X1) = Var(X2) = Var(X3) = 0. 12= 0. 01

Find the sum of the variances to find the variance of the sum. Var(X) = VarX1+ VarX2+ VarX3 = 0. 01 + 0. 01 + 0. 01 = 0. 03 Recall that the standard deviation is the square root of the variance. Find the standard deviation. SD(X) = Var(x) = 0. 03 = 0. 17

Therefore, the standard deviation is 0. 17 eggs.What assumptions did you have to make about the eggs in order to answer this question? The variance for the sum of random variables is only the sun of variances of each random variable in certain cases. Review the assumption that must be made to allow the variance to be the sum of the individual variances. 

An insurance company estimates that it should make an annual profit of $260 on each homeowner’s policy written, with a standard deviation of $6000.

Why is the standard deviation so large? Home insurance is used to protect the owner financially in the event of a problem. If a catastrophe occurs, then the insurance company will cover the cost of the damage. If a catastrophe never occurs, then the insurance company pays nothing. Meanwhile, the owner pays the insurance company at regular intervals whether or not a catastrophe occurs. The expected value is the mean annual profit on all of the policies and the standard deviation is a measure of how much annual profits can differ from the mean. Use this information with the fact that claims are rare, but very costly, occurrences.

If the company writes only four of these policies, what are the mean and standard deviation of the annual profit?

Let X1,X2, X3,…,Xn represent the annual profit on the n policies and let X be the random variable for the total annual profit on n polices written.

X=X1+X2+ X3+…+Xn The expected value of the sum is the sum of the expected values. Find the expected value of the annual profit on each policy.

EX1=EX2=EX3=EX4=$260 Now find the sum of the expected values.

EX=EX1+EX2+EX3+EX4 =260+260+260+260 = $1040

Therefore, the mean annual profit is $1040 To find the standard deviation of the annual profit, use the fact that te variances of the sum of independent variables is the sum of their individual variances. First find the variance for each policy.

The variance for the policy is the

square of the standard deviation.

VarX1=VarX2=VarX3=VarX4=60002=36,000,000 VarX=VarX1+VarX2+VarX3+VarX4 = 4(36,000,000) = 144,000,000

Evaluate the square root of the variance to find the standard deviation.  SDX=VarX =144,000,000 =$12,000

Therefore, the standard deviation is $12,000 c) If the company writes 10,000 of these policies, what are the mean and standard deviation of annual profit? The expected value of the sum is the sum of the expected values. The expected value of each policy was found earlier. EX1=EX2=EX3=... =EX10,000=$260 Now find the sum of expected values.

EX=EX1+EX2+EX3+... +EX10,000 10,000(260) =$2,600,000

Therefore, the mean annual profit is $2,600,000 To find the standard deviation of the annual profit, use the fact that the variance of the sum of independent variables is the sum of their individual variances. First find the variance for each policy. Evaluate whether the distance of $0 from the mean is convincing enough to determine whether or not the company will be profitable.

What assumptions underlie your analysis? Can you think of circumstances under which those assumptions might be violated? The variance of the sum of random variables is only the sum of the variances of each random variables in certain cases. Review the assumption that must be made to allow the variance to be the sum of the individual variances. Then chose the situation that would create an association among policy losses. A farmer has 130 lbs. of apples and 60 lbs. f potatoes for sale. The market price for apples (per pound) each day is a random variable with a mean of 0. 8 dollars and a standard deviation of 0. 4 dollars. Similarly, for a pound of potatoes, the

mean price is 0. 4 dollars and the standard deviation is 0. 2 dollars. It also costs him 5 dollars to bring all the apples and potato’s to the market. The market is busy with shoppers, so assume that he’ll be able to sell all of each type of produce at the day’s price. Define your random variables, and use them to express the farmer’s net income. A random variable’s outcome is bases on a random event.

Therefore let the random variables represent the factors that will be randomly determined each day. The random variables should represent the market prices of the two items. A = price per pound of apples P = price per pound of potatoes The profit is equal to the total income minus the total cost. The income is found by multiplying the market price for apples by the total number of pounds sold and adding it to the product of the market price for potatoes and the number of pounds of potatoes sold.