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 0.08 0.22 0.3 0.28 0.12

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

a. X 2

b. X > 1   

c. X 1

d. X 1

1)What is the probability of this event?

Describe the event X 2 in words.

a. no more than three nonword errors

b. less than 2 nonword errors    

c. more than 2 nonword errors

d. no more than two nonword errors

2)What is its probability?

3)What is the probability that X < 2?

Explanation / Answer

f=   1  
fx =   2.14  
      
Mean = fx / f =   2.14  
Mean square = f x^2 / f =   5.86  
      
Varriance = (Mean square) - (Mean)^2      
      
Varriance = f x^2 - Mean^2 =   1.28  
Stadard Dev= Var =   1.131  

1.
c. X 1
2.
d. no more than two nonword errors
3.
P(X<=2) = P(X=0) + P(X=1) + P(X=2) = .08 + 0.22 + 0.3 = 0.60
4.
P(X < 2) = P(X=0) + P(X=1) = .08 + 0.22 = 0.30

Values ( X ) Frequency(f) fx ( X^2) f x^2 0 0.08 0 0 0 1 0.22 0.22 1 0.22 2 0.3 0.6 4 1.2 3 0.28 0.84 9 2.52 4 0.12 0.48 16 1.92

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