# Calculating Expected Value and Descriptive Statistics

1. A government has specialist who analyze the frequencies of letters of the alphabet in an attempt to decipher intercepted messages. In standard English text, a particular letter used at a rate of 6.8%.

a) Find the mean and standard deviation for the number of times this letter will be found on a typical page of 2000 characters.

b) In an intercepted message, a page of 2000 characters is found to have the letter occurring 155 times. Is this unusual?

2. Assume that a procedure yields a binomial distribution with n trails and the probability of success for one trail is p. Use the given values of n and p to find the mean and standard deviation. Also use the range rule of thumb to find the minimum usual value µ-2σ and the maximum usual value µ+2σ.

N=1435, p=1/5

µ=___

σ=____(round to one decimal place if needed)

µ-2σ=___ (round to one decimal place if needed)

µ+2σ=____(round to one decimal place if needed)

3. An insurance company charges a 21 year year old male a premium of $250 for a one year $50,000 life insurance policy. A 21 year old male has a 0.9985 probability of living for a year.

a) From the perspective of a 21 year old male (or his estate) what are the values of the two different outcomes? If he lives is____dollars If he dies is____dollars

b) What is the expected value for a 21 year old male who buys the insurance? Expected value____dollars

c) What would be the cost of the insurance if the company just breaks even ( in the long run with many such policies) instead of making a profit?____dollars

#### Solution Preview

1. A government has specialist who analyze the frequencies of letters of the alphabet in an attempt to decipher intercepted messages. In standard English text, a particular letter used at a rate of 6.8%.

a) Find the mean and standard deviation for the number of times this letter will be found on a typical page of 2000 characters.

Mean=2000*6.8%=136, and sd=sqrt(2000*6.8%*93.2%)=11.2584

b) In an intercepted message, a page of 2000 characters is found to have the letter occurring 155 times. Is this ...

#### Solution Summary

The solution gived detailed steps on solving some questions on the topic of descriptive statistics. All formula and calculations are shown and explained.