Spell-checking software catches \"nonword errors\" which result in a string of l

Question

Spell-checking software catches "nonword errors" which result in a string of letters that is not a word, as when "the" is type "teh." When undergraduates are asked to write a 250 word essay (without spell checking), the number X of nonword errors has the following distribution: a. In the table shown above the probability of exactly 4 errors is not given. Using what you know about probability distributions, what is the probability of exactly 4 errors? b. What is the probability of at least l nonword error? c. Find the expected value of this distribution. How many nonword errors can you expect from a typical paper written under the previously mentioned conditions?

Explanation / Answer

a) The sum of all probabilities should be equal to 1. Therefore we get:

P(X=4) = 1 - 0.3 - 0.25 - 0.2 -0.17 = 0.08

Therefore 0.08 is the required probability here.

b) The probability of at least 1 nonword error here is:

= 1- Probability of no error

= 1 - P(X=0)

= 1 - 0.3 = 0.7

Therefore 0.7 is the required probability here.

c) The expected value of the distribution is computed bu multiplying the probabilities of occurence of each number of by the number of errors:

E(X) = 0*0.3 + 1*0.25 + 2*0.2 + 3*0.17 + 4*0.08

E(X) = 0.25 + 0.4 + 0.51 + 0.32 = 1.48

Therefore the expected number of error is 1.48

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