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 ofX O 1234 Probability 0.08 0.17 0.31 0.3 0.14 (a) Sketch the probability distribution for this random variable Probability Probability 0.35 0.30 0.25 0.20 0.15 0.10 0.05 0.30 0.25 0.20 0.15 0.10 0.05 Errors Errors 3 Probability Probability 0.30 0.25 0.20 0.15 0.10 0.05 0.35 0.30 0.25 0.20 0.15 0.10 0.05 Errors Errors 3 (b) Write the event "at least one nonword error in terms of X

Explanation / Answer

This is a case of discrete probability distribution

a) for 0, probability is 0.8 which is shown by a), c) and d) , for 1 probability is 0.17, which is shown correctly by C) alone thus it is correct answer

b) answer is c x>=1 (atleast includes 1 also). Probablity is 1-P(x=0) which is 1-0.08 or 0.92

c) D) no more than 2

probability is P(x=0)+P(x=1)+P(x=2)=0.08+0.17+0.31 =0.56

probability is P(x=0)+P(x=1) =0.08+0.17 =0.25

c)

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