10 pts 7 580000 when she dies Let X Bettys the net profit Ba

[10 pts.] 7 580,000 when she dies. Let X Betty\'s the net profit. Based on mortality 0.995 chance that Betty will live until the next year Betty Binomial pays $900 annually for a life insurance policy which is worth on mortality data, there is a (a) Fill in the probability distribution Lives Dies Put the X column in L1 and the P(X) column in L.2 and use your calculator to find the expected value and the standard deviation of the distribution. Use the correct symbols. What is the interpretation of the expected value ? [10 ptsJ 8 Write all probabilities the calculator command that you use to do the following In a recent study it was found that 85% of all airline passengers actually arrive for the flight If we randomly select 20 airline passengers randomly from the huge population of 8 Write all probabilities symbolically in terms of the random variable X and show all airline travelers.... (a) Explain why this sampling process an example of trials that are approximately independent Ifx-#fpassengers who arrive for the flight, identify the n, p and q and f this binomial random variable (b) . .for the flight

Solution

7)

we know that when she die she will pay $80,000 and if she lives she will pay $900

the probability of she lives is 0.995 and the probability of she dies is 1-0.995 = 0.005

Expect value is: 900*0.995 + 80,000*0.005 = 1,295.5

x^2*P(x)= 900^2*0.995 + 80,000^2 * 0.005 = 32,805,950

standard deviation= sqrt(32,805,950 - 1,295.5)

standard deviation: 5,727.53

The expected value represents the average value which is expected, by repeating the experiment independently a lot of times

So for this case presents the average value which is expected to pay in the posibilities of dies and lives

8)

Well As we know this is a binomial distribution and for the binomial model use the bernoulli trials

Independent means that the outcome of one trial does not affect the outcome of the other,

and we can see that are approximately independents because

each passenger can either a arrive for the flight or a non-arrive for the flight; arrive for the flight being a success here

if a passenger can arrive for the flight not affect that other passenger can arrive or non arrive for the flight

N= sample that is 20

p= success that is 0.85

q= fail that is 1-0.85 = 0.15

	X	P(x)
lives	900	0.995
Dies	80,000	0.005