Question

Spell‑checking software catches nonword errors that result in a string of letters that is not a word, as when "the" is typed as "teh." When undergraduates are asked to type a 250250‑word essay, without spell‑checking, the number ?X of nonword errors has the provided distribution.

Value of ?X	00	11	22	33	44
Probability	0.10.1	0.20.2	0.30.3	0.30.3	0.10.1

(a) Is the random variable ?X discrete or continuous? Why?

Discrete, because we do not know the number of errors in advance.

Discrete, because it has a finite number of possible values: 0,1,2,3,40,1,2,3,4 .

Continuous, because there can be all sort of errors.

Continuous, because all the probabilities are between 00 and 11 .

(b) Which statements are equivalent to the event "at least one nonword error" in terms of ?X ? Select all that apply.

?≥1X≥1

?≠0X≠0

?≥0X≥0

?<1X<1

?>0X>0

What is the probability of the "at least one nonword error" event? Enter your answer within one decimal place.

?(nonword error)P(nonword error) =

Which one of the statements describes the event ?≤2X≤2 ?

less than 22 nonword errors

at least 22 nonword errors

no more than 22 nonword errors

more than 22 nonword errors

(c) What is the probability of the event ?≤2X≤2 ? Enter your answer within one decimal place.

?(?≤2)=P(X≤2)=

What is the probability of the event ?<2X<2 ? Enter your answer within one decimal place.

?(?<2)=P(X<2)=

Question Source: Moore, The Basic Practice Of Statistics, 8e|Publisher: W.H. Freeman

Answer 1

Solution :

(a)

Discrete, because it has a finite number of possible values: 0,1,2,3,4

(b)

The statements are equivalent to the event "at least one nonword error" in terms of ? is,

X 1

P(nonword error) = P(X 1) = 1 - P(X < 1) = 1 - P(X = 0) = 1 - 0.1 = 0.9

P(nonword error) = 0.9

(c)

The probability of the "at least one nonword error" event is ,

X 2

P(X 2) = P(X = 0) + P(X = 1) + P(X = 2) = 0.1 + 0.2 + 0.3 = 0.6

P(X 2) = 0.6

P(X < 2) = P(X = 0) + P(X = 1) = 0.1 + 0.2 = 0.3

P(X < 2) = 0.3