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.

Value of X 0 1 2 3 4

Probability 0.06 0.16 0.3 0.25 0.23

(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

1) What is the probability of this event?
______

(c) Describe the event X 2 in words.

* no more than three nonword errors

*less than 2 nonword errors    

*more than 2 nonword errors

*no more than two nonword errors

1) What is its probability?
__________

Explanation / Answer

A) Option-C is correct

B) Option-C) X > 1

P(X > 1) = P(x = 1) + P(X = 2 ) + P(x = 3) + P (X = 4)

= 0.16 + 0.3 + 0.25 + 0.23 = 0.94

C) X < 2 , means not more than two nonwards error.

Option-D)

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

= 0.06 + 0.16 + 0.3 = 0.52

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