Spell-checking software catches \"nonword errors,\" which are strings of letters

Question

Spell-checking software catches "nonword errors," which are strings of letters that are not words, as when "the" is typed as "eth." When undergraduates are asked to write a 250-word essay (without spell-checking), the number X of nonword errors has the following distribution.

(a) Sketch the probability distribution for this random variable.

(b) Write the event "at least one nonword error" in terms of X.

X 2

X > 1

X 1

X 1

What is the probability of this event?


(c) Describe the event

X 2

in words.

no more than three nonword errorsless than 2 nonword errors     more than 2 nonword errorsno more than two nonword errors

What is its probability?


What is the probability that

X < 2?

Explanation / Answer

a) First sketch is pdf of above random variable.

b) The event "at least one nonword error" in terms of X is X 1

P(X 1) =1 - P(X=0)

c) X 2 means no more than 2 non words error

P(X<2) = P(X=0) + P(X=1)

= 0.26

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