1. The following probability tree characterizes prospects that may occur after choosing a given alternative. The profit (expressed in thousands of dollars) is presented at the end of the tree. K$ 30 High Demand 0.3 0.7 Low Demand High Cost 0.2 {Profit <= 80 K$|& } {20 <= Profit <= 70 & } {Profit >= 30 K$|& } 0.8 Low Cost High Cost 0.5 0.5 Low Cost a. Plot the probability mass function for profit b. Plot the cumulative probability for profit. c. Plot the excess cumulative probability for profit. d. Determine: Sun 0.6 0.4 Rain Sun 0.6 0.4 Rain Sun 0.6 0.4 Rain Sun 0.6 0.4 Rain 40 100 110 -10 0 20 30

The lowest portfolio risk will result when the asset returns are perfectly positively correlated.   Select one: True False

What is the probability that the total of two randomly chosen numbers exceeds 3, where the first number is chosen from a uniform distribution between 0 and 2, and the second number is selected from an exponential distribution with a mean of 1?

Recall that Benford's Law claims that numbers chosen from very large data files tend to have "1" as the first nonzero digit disproportionately often. In fact, research has shown that if you randomly draw a number from a very large data file, the probability of getting a number with "1" as the leading digit is about 0.301. Now suppose you are the auditor for a very large corporation. The revenue file contains millions of numbers in a large computer data bank. You draw a random sample of n = 226 numbers from this file and r = 87 have a first nonzero digit of 1. Let p represent the population proportion of all numbers in the computer file that have a leading digit of 1. 1) Test the claim that p is more than 0.301. Use α = 0.10. 2) What is the value of the sample test statistic? (Round your answer to two decimal places.)  3) Find the P-value of the test statistic. (Round your answer to four decimal places.)  4) If p is in fact larger than 0.301, it would seem there are too many numbers in…

The useful life of Johnson rods for use in a particular vehicle follows an exponential distribution with an average useful life of 5.2 years.You have a three-year warranty on your vehicle’s Johnson rod. What is the probability that the Johnson rod doesn’t fail before then? That is, what is the probability that its useful life doesn’t end before three years?b.If the vehicle manufacturer wants to limit the number of claims on the three-year warranty to 20%, what should the average useful life of the Johnson rod be?

(first part of question is attached) (e) What is the probability that the sample proportion of students of adults living with parents or other relatives is higher than 0.3? (f) What is the probability that the sample proportion of adults living alone is between 0.1 and 0.15?

Benford's Law claims that numbers chosen from very large data files tend to have "1" as the first nonzero digit disproportionately often. In fact, research has shown that if you randomly draw a number from a very large data file, the probability of getting a number with "1" as the leading digit is about 0.301. Suppose you are an auditor for a very large corporation. The revenue report involves millions of numbers in a large computer file. Let us say you took a random sample of n = 250 numerical entries from the file and r = 60 of the entries had a first nonzero digit of 1. Let p represent the population proportion of all numbers in the corporate file that have a first nonzero digit of 1. Test the claim that p is less than 0.301 by using α = 0.01. What does the area of the sampling distribution corresponding to your P-value look like?         a. The area in the right tail of the standard normal curve.   b. The area not including the right tail of the standard normal curve.…

Please solve (b) only!

Question 15 The percent of fat calories that a person in America consumes each day is normally distributed with a mean of about 36 and a standard deviation of 10, Suppose that one individual is randomly chosen. Let X percent of fat calories. FEB 7. sC 80 000 000 F1 F2 F3 F4 F5 F6 ! @ % 1 2 3 4 5 6 %24