The English alphabet has 26 letters. There are 6 vowels. (a, e, i, o, u, and...

The English alphabet has 26 letters. There are 6 vowels. (a, e, i, o, u, and sometimes y). Suppose we randomly select 8 letters from the alphabet without replacement. Let X = the number of vowels chosen (including y as a vowel).

a. How many possible ways are there to select the 8 out of 26 letters (order does not matter) without replacement?
b. What is the probability that X = 2
c. What is the probability that X=1?
d. What is the probability that X < 3?
e. What is the expected value of X?
f. What is the standard deviation of X?
g. What is the probability that X is within 1.1 standard deviations of its expected value?
h Execute the R command "sample(letters,8)". How many vowels did you get?

Expert Solution

Answer h. We get 2 vowels

orchestra answered 1 year ago

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