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Solved: Deciphering Messages The Central Intelligence
Chapter 5, Problem 16BSC(choose chapter or problem)
The Central Intelligence Agency has specialists who analyze the frequencies of letters of the alphabet in an attempt to decipher intercepted messages that are sent as ciphered text. In standard English text, the letter e is used at a rate of 12.7%.
a. Find the mean and standard deviation for the number of times the letter e will be found on a typical page of 2600 characters.
b. In an intercepted ciphered message sent to France, a page of 2600 characters is found to have the letter e occurring 290 times. Is 290 unusually low or unusually high?
Questions & Answers
QUESTION:
The Central Intelligence Agency has specialists who analyze the frequencies of letters of the alphabet in an attempt to decipher intercepted messages that are sent as ciphered text. In standard English text, the letter e is used at a rate of 12.7%.
a. Find the mean and standard deviation for the number of times the letter e will be found on a typical page of 2600 characters.
b. In an intercepted ciphered message sent to France, a page of 2600 characters is found to have the letter e occurring 290 times. Is 290 unusually low or unusually high?
ANSWER:Step1 of 2:
The Central Intelligence Agency has specialists who analyze the frequencies of letters of the alphabet in an attempt to decipher intercepted messages that are sent as ciphered text. In standard English text, the letter e is used at a rate of 12.7%.
That is p = 0.127
a). The mean and standard deviation for the number of times the letter e will be found on a typical page of 2600 characters is given by
Consider a random variable “x” following a binomial distribution with sample size “n” and proportion “p”.
\(\text { i,e. } X \sim B(n, p)\)
Where,
n = 2600 and p = 0.127.
\(\begin{aligned} q & =1-p \\ & =1-0.127 . \\ & =0.873 \end{aligned}\)
Probability mass funct