Question

(1 point) An insurance company knows that in the entire population of millions of homeowners, the mean annual loss from fire is ? = $150 and the standard deviation of the loss is ? = $900. The distribution of losses is strongly right skewed: most policies have $0 loss, but a few have large losses. If the company sells 10,000 policies, what is the probability that it can safely base its rates on the assumption that its average loss will be no greater than $170?

Answer 1

1)
P(x < 170)

z = ( x -mean)/(s/sqrt(n))
= ( 170 - 150)/(900/sqrt(10000)
= 2.2222

P(x <170) = P(z < 2.2222) = 0.9869

2)

a)

3,4,6,10

b)

mean = 23/4 = 5.75

c)

(3,4) (3,6) (3,10) ( 4,6) ( 4,10) ( 6,10)

d) mean of sample size 2 = 3.5 , 4.5 , 6.5 , 5 ,7 ,8

mean of samping distribution = 5.75