2. 120 points) A mail-order computer business has five telephone lines. Let X de
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Question
2. 120 points) A mail-order computer business has five telephone lines. Let X denote the number of lines in use at a specified time. Suppose the pmf of X is as given in the accompanying table. 0.18 0.15 0.20 0.22 0.25 Calculate the probability of each of the following events. a. at least 3 lines are in use b. between 2 and 4 lines, inclusive, are not in use 120 points] Consider a class of 20 students. Answer the following questions. 3. Findings of a research states that the probability of an individual who is left-handed is 0.20 What is the probability that the number of left-handers in the class is less than 4? a. b. If you select two students randomly, what is the probability that both of them are left-handers?Explanation / Answer
QUestion 3
(A) Pr(at least 3 lines are in use) = Pr( X = 3) + Pr( X = 4)
= 0.22 + 0.25
= 0.47
(B) Here it is asked that from 2 to 4 are not in use that means we can use 0 and 1 number of telephone lines
Pr(X = 0 & X = 1) = Pr( X = 0 ) + Pr(X =1)
= 0.18 + 0.15 = 0.33
Question 4
Number of studnets in class n = 20
Pr(left handed) = 0.20
The given distibution is binomial distribution
(a) Pr(NUmber of left handers are less than 4) = Pr(X < 4) = BINOMIAL (X < 4 ; 20 ; 0.2)
By checking binomial table
Pr(X <4) = 0.4114
(b) If two students chosing randomly than the probability that both will be left handed = Pr(First student is left - handed ) * Pr(second student is also left handed) = 0.2 * 0.2 = 0.04
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