Answered

Welcome to Westonci.ca, the Q&A platform where your questions are met with detailed answers from experienced experts. Get immediate answers to your questions from a wide network of experienced professionals on our Q&A platform. Join our platform to connect with experts ready to provide precise answers to your questions in different areas.

In any​ year, the weather can inflict storm damage to a home. From year to​ year, the damage is random. Let Y denote the dollar value of damage in any given year. Suppose that in 95​% of the years Y​ = ​$0​, but in 5​% of the years Y ​= ​$20,000.
A. The mean of the damage in any year is ​$__. nothing. The standard deviation of the damage in any year is ​$____.
B. Consider an​ "insurance pool" of 100 people whose homes are sufficiently dispersed so​ that, in any​ year, the damage to different homes can be viewed as independently distributed random variables. Let barY denote the average damage to these 100 homes in a year. The expected value of the average damage barY, is ​$____. The probability that exceeds ​$is____.

Sagot :

ogorwyne

Answer:

a. mean = 1000

standard deviation = 4358.9

b. expected value of average damage bar Y = 1000

probability bar y exceeds 2000 = 0.011

Step-by-step explanation:

we have p1 = 95%, y1 = 0, p2 = 5%, y2 = 20000

Mean = (0.95 * 0) + (0.05 * 20000)

= 1000

var(y) = E(y²) - E(Y)²

= we solve for E(y)²

= 0²*0.95 + 20000²*0.05

= 0 + 20000000

then the variance of y = 20000000 - 1000²

=20000000-1000000

= $19000000

standard  deviation is the square root of variance

= √19000000

= 4358.9

2.

a. Expected value of average is also the mean = 1000

b. we are to find probability that barY exceeds 2000

[tex]z=\frac{2000-1000}{\sqrt{19000000/100} }[/tex]

= 1000/435.889

= 2.29

1-p(z≤2.29)

= 1 - 0.989

= 0.011

so the probability that barY exceeds 2000 is 0.011

Thanks for using our service. We're always here to provide accurate and up-to-date answers to all your queries. We appreciate your time. Please come back anytime for the latest information and answers to your questions. Thank you for visiting Westonci.ca. Stay informed by coming back for more detailed answers.