Deciphering Messages 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 r is used at a rate of 6%.
a. Find the mean and standard deviation for the number of times the letter r will be found on a typical page of 2600 characters.
b. In an intercepted ciphered message sent to Iran, a page of 2600 characters is found to have the letter r occurring 178 times. Is this unusually low or high?
Step 1 of 1
On a typical of n=2600 characters, the probability of success p=6%.
Then p=6/100 = 0.06 because the letter is used at a rate of 6%.
This gives the probability of failure, q = 1 - p.
q = 1 - p = 1 - 0.06 =0.94
Therefore the mean and the standard deviation for the given binomial distribution is given as
The Mean of the formula is
μ =(2600) (0.06)
μ = 156
Therefore the mean μ =156
The formula of the standard deviation is given by
σ = 12.1095
Therefore the standard deviation is σ = 12.1095
We know that μ =156 and σ = 12.1095
Maximum usual values μ + 2σ and Minimum usual values μ-2σ
= ( μ ± 2σ)
= (156 ± 2(12.1905) )
= (156 ± 24.381 )
= (156+24.381 , 156-24.381 )
= (180.381 , 131.619 )
Any value in between 180.381 and 131.619 is not considered unusually since it lies with 2 standard deviation from the mean.
Yes.In an intercepted ciphered message sent to Iran, a page of 2600 characters is found to have the letter r occurring 178 times.
A value of 178 could not be considered unusually.