The law of large numbers tells us what happens in the long run. Like many games of chance, the numbers racket has outcomes so variable-one three digit number wins $600 and all others win nothing-that gamblers never reach "the long run". Even after many bets, their average winnings may not be close to the mean. For the numbers racket, the mean payout for single bets is $0.60 and the standard deviation of payouts is about $18.96. If Joe plays 350 days a year for 40 years, he makes 14,000 bets.

1. What are the mean and standard deviation of the average payout mean that Joe receives from his 14,000 bets?

2. The central limit theorem says that his average payout is approx Normal with the mean and standard deviation you found in #1. What is the approximate probability that Joe's average payout per bet is between $0.50 and $0.70? You see that Joe's average may not be very close to the mean $0.60 even after 14,000 bets.

Solution Preview

(1) Mean, x-bar = mu = 0.60

SD, s = sigma/sqrt n = ...

Solution Summary

A Complete, Neat and Step-by-step Solution is provided.

... 5. Suppose that an insurance agent claims that the average life insurance ... A sample of 45 customers yields a mean of x = $575 and a standard deviation of s ...

... The mean amount of money that an individual expects ... On average, people lose money by playing the lottery. ... Part 2 The standard deviation is calculated as follows ...

... what is the probability that their average catch is ... From the survey, we found the mean of the population is approximately 32 with a standard deviation of 4 ...

... c. what is the average number of customers in line? ... The process has a mean of .997 and a standard deviation of .001 inch. Is the process capable? ...

... an insurance agent for State Ranch claims that the average life insurance ... A sample of 40 customers yields a mean of x =$475 and a standard deviation of s ...

... There are deviations from these assumptions as seen ... having "irrational exuberance." What he meant was that ... 2 = or 10.16% Answer: Standard deviation of portfolio ...

... relationship between dividend payout and shareholders ... significant difference in average market value ... been used are Mean, Standard Deviation, multiple regression ...

... a. expected returns b. standard deviations c. covariances d. all of the ... This means that he would ... inverse relationship between risk and expected average return e ...

...mean and median valuation errors (absolute deviation of value ... we make assumptions that are standard in the ... We estimate portfolio betas as the portfolio means. ...