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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.

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