The Central Intelligence Agency has specialists who analyze the frequecnies of letters of the alphabet in an attempt to decipher intercepted messages. In standard English text, the letter e is used most often at a rate of 12.702%. In an intercepted message sent to Iraq, a page of 1516 characters is found to have the letter e occurring 175 times. Is this unusual? What function would be entered onto a TI-84 CE Plus calculator to solve this?
Answer
it is a binomial distribution case with probability p = (12.702/100) = 0.12702
total number of trials is n = 1516 and number of successes is k = 175
using function binompdf(n,p,k)
setting n = 1516, p = 0.12702 and k = 175
this implies
= binompdf(1516,0.12702,175)
= 0.0125
Yes, it is unusual because the probability of getting 175 e's from 1516 characters has a p value of 0.0125, which is less than 0.05 limit.
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