Agovernment 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 5.7%. a. find the mean and standard deviation for the number of times this letter will be found on a typical page of 1600 characters. muequals 91.2 (do not round.) sigmaequals 9.3 (round to one decimal place as needed.) b. in an intercepted message, a page of 1600 characters is found to have the letter occurring 102 times. is this unusual? \

A) μ = 91.2; σ = 9.3

B) No

Step-by-step explanation:

To find the mean, μ, we use the formula

μ = np, where n is the sample size and p is the probability of success (percentage of times the letter is used).

This gives us

μ = 0.057(1600) = 91.2

To find the standard deviation, we use the formula

σ = √(np(1-p)

This gives us

σ = √(1600×0.057×(1-0.057))

= √(1600×0.057×0.943) = √86.0016 = 9.2737 ≈ 9.3≈

Any value that is more than two standard deviations from the mean is considered unusual.  The value 102 is

(102-91.2)/9.3 = 10.8/9.3 = 1.16 standard deviations from the mean.  This is not statistically unusual.

in mathematics, a function is a relationship between two variables such that the value of one of the variables, called the dependent variable, is determined by the value of the other variable, called the independent variable. there is a specific term we use to describe the set of independent variables of a function.