Question

7 - The annual claims made by clients on their insurance policies have an average of 8 million dollars and a standard deviation of 1.5 million dollars. If the amounts can be assumed to have a normal distribution, find the probability that the annual claims in 1 year is

(a) Greater than 10 million dollars,

(b) Between 6 million and 9 million dollars,

(c) Either less than 7 million or greater than 10 million dollars and,

(d) Find the annual claims that have 35% chance of being more than other claims.

8 - Data collected at Toronto Pearson International Airport suggests that an exponential distribution with mean value 3.25 hours is a good model for rainfall duration.

a. What is the probability that the duration of a particular rainfall event at this location is at least 2 hours?

b. What about the duration of a particular rainfall event is at most 3 hours?

c. What about the duration of a particular rainfall event is between 2 and 3 hours?

d. What about having no rainfall in a particular 2 hours observation?

9 - The time X (min) for a lab assistant to prepare the equipment for a certain experiment is believed to have a uniform distribution with A=35 and B=47.

a. Determine the pdf of X and sketch the corresponding density curve.

b. What is the probability that preparation time is less than 38 min?

c. What is the probability that preparation time is within 2.5 min of the mean time?

d. For any a such that 35

Answer 1

dear student we can provide you with the solution of 4 sub question at a time.

7) Let X be the annual claims made by clients on their insurance policies that is assumed to be normally distributed with where these are in million dollars

a) the probability that the annual claim is greater than 10 million dollar is

(using excel formula 1-NORM.S.DIST(1.3333,TRUE) )

b) the probability that the annual claim is between 6 and 9 million dollar is

( using excel formula =NORM.S.DIST(0.6667,TRUE)-NORM.S.DIST(-1.3333,TRUE))

c)the probability that the annual claim is either less than 7 or greater than 10 million dollars

(using excel formula NORM.S.DIST(-0.6667,TRUE) )

d) Let A be the annual return that is 35% above the other clims

critical Z value corresponding to the probability can be found using the excel formula (=NORM.S.INV(0.35) )

milion dollars