Question

A business has six customer service telephone lines. Let x denote the number of lines in use at a specified time. Suppose that the probability distribution of x is as follows. x 0 1 2 3 4 5 6 p(x) 0.10 0.15 0.20 0.25 0.20 0.07 0.03 Write each of the following events in terms of x, and then calculate the probability of each one. (a) At most three lines are in use. (b) Fewer than three lines are in use. (c) At least three lines are in use. (d) Between two and five lines (inclusive) are in use. (e) Between two and four lines (inclusive) are not in use. (f) At least four lines are not in use.

          A business has six customer service telephone lines.
Let x denote the number of lines in use at a specified time. Suppose that the probability distribution of x is as follows.
x
0
1
2
3
4
5
6
p(x)
0.10
0.15
0.20
0.25
0.20
0.07
0.03
Write each of the following events in terms of x, and then calculate the probability of each one.
(a) At most three lines are in use.
(b) Fewer than three lines are in use.
(c) At least three lines are in use.
(d) Between two and five lines (inclusive) are in use.
(e) Between two and four lines (inclusive) are not in use.
(f) At least four lines are not in use.

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Added by Tammy R.

Elementary Statistics a Step by Step Approach

Allan G. Bluman 9th Edition

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Solved by Expert David Nguyen

12/21/2021

Step 1

- \( P(X \leq 3) = P(X=0) + P(X=1) + P(X=2) + P(X=3) \) - \( P(X \leq 3) = 0.10 + 0.15 + 0.20 + 0.25 = 0.70 \) Show more…

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A business has six customer service telephone lines. Let x denote the number of lines in use at a specified time. Suppose that the probability distribution of x is as follows. x 0 1 2 3 4 5 6 p(x) 0.10 0.15 0.20 0.25 0.20 0.07 0.03 Write each of the following events in terms of x, and then calculate the probability of each one. (a) At most three lines are in use. (b) Fewer than three lines are in use. (c) At least three lines are in use. (d) Between two and five lines (inclusive) are in use. (e) Between two and four lines (inclusive) are not in use. (f) At least four lines are not in use.

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Transcript

00:01 Hi, i'm david and i'm here to help you answer your question.

00:04 Now let me pick up your question here.

00:06 In this question we're given the x is the number of the lines in used at a specified time.

00:15 And we're given the table for the distribution.

00:18 So let me write it down here for you.

00:20 X, probability of x.

00:24 X can have a value of the 0, 1, 2, 3, 4, and 5 now the corresponding probability will be 0 .1 0 .15 0 .2 0 .25 .15 0 .2 0 .25 0 .2 0 .25 0 .2 0 .027 0 .7.

00:52 So we have will be 6 as well.

00:56 We have another 1 0 .03.

00:59 3 and that will be the table for the distribution function.

01:04 Now we have the question a.

01:07 Once you find the probability that at most three lines are used, so x will be almost small equal to 3.

01:15 So we sum up on the value from 0 to 3 here.

01:19 So equal to 0 .1 plus 0 .15 plus 0 .0 .25.

01:26 If we do it, we have equal to the 0 .2.

01:29 3 plus 0 .4 equal to 0 .7.

01:34 And that's what be the answer for the a.

01:37 Now for the b, fewer than three lies and in use.

01:43 So x will be smaller than three lies.

01:51 And then it will equal to x can have our only value from 02 only.

01:57 So it will be 0 .1 plus 0 .15 plus 0 .0 .2.

02:02 Then we get equal to the 0 .45.

02:06 And that's what will be the answer for the b.

02:09 Now for the c, and these two lines are in use...

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