Question

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 6.8​%.
a. Find the mean and standard deviation for the number of times this letter will be found on a typical page of 3000 characters.

Answer 1

let n be the number of times letter be found (1800), p be the success rate (0.068), and q be the failure rate (1 - 0.068 = 0.932)  

mean = np = 1800 x 0.068 = 122.4  

standard deviation = √(npq) = √(1800 x 0.068 x 0.932) = 10.6807414