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.

without spell-checking the number X of nonword errors has the eth when undergraduates are asked to write a 2SO word essay the is typed as which are strings of letters that are not words, as when Spell-checking soft are catches following distribution non ordrrors, Value of x O Probability 0.10 | 0.29 0.29 0.20 0.12 (a) Sketch the probability distribution for this random variable. Probablity 0.3 0.2 Probablity Probablity 035 030 0.25 0.20 0.15 0.10 0.0 0.25 0.2 0.1 0.10 0.05 0.10 0.10 0.0 Errors Errors Prrors Errors (b) Write the event 'at least one nonword error" in terms of X. What is the probability of this event? (c) Describe the event X3 in words o no more than four nonword errors O less than three nonword errors o more than three nonword errors o no more than three nonword errors What is its probablity? What is the probability that X 3?

Explanation / Answer

a) We see that the probability for 0 is 0.1 which is correctly shown by graph 1 hence its correct

b) it is x>=1 which is option C . Also, its value is 1-P(x<1) , from the table we get 1-0.1 or 0.9

c) answer is D) no more than 3, probability is 1-P(x>3) which is 1-0.12 or 0.88

P(x<3)=P(x=0)+P(x=1)+P(x=2)=0.10+0.29+0.29=0.68

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