8.A government agency has specialists who analyze the frequencies of letters of
ID: 3075065 • Letter: 8
Question
8.A government agency has specialists who analyze the frequencies of letters of the alphabet in an attempt to decipher intercepted messages. In standard English text, a particular letter is used at a rate of 7.2%.
a. Find the mean and standard deviation for the number of times this letter will be found on a typical page of 3000 characters.
mu=
sigma=
b. In an intercepted message, a page of 3000 characters is found to have the letter occurring 272 times.
Is this unusual?
A.Yes comma because 272 is greater than the maximum usual value.
B.No comma because 272 is within the range of usual values.
C.Yes, because 272 is within the range of usual values.
D.Yes comma because 272 is below the minimum usual value.
Explanation / Answer
SOLUTION:
Given n=3000, p=0.072 , q=1-0.072=0.928
Mean= n*p = 3000*0.072 = 216
Standard devaition = sqrt(n*p*q) =sqrt(200.448) = 14.16
b.)
In an intercepted message, a page of 3000 characters is found to have the letter occurring 272 times.
Is this unusual?
yes this is unusual because 272 is greater than the maximum usual value (i.e mean+3*sd=258).
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