Question

An accounting office has six incoming telephone lines. Let the random variable X = the number of busy lines. The probability distribution function for X is given below.

x | 0 | 1 | 2 | 3 | 4 | 5 | 6 |

f(x) | 0.052 | 0.154 | 0.232 | 0.240 | ? | 0.105 | 0.043 |

(a). Find the Probability that there are 4 busy lines?

My Ans: It should be 0.826, (1-sum of others).

I'm struggling to answer the rest of them.

(b). Find the expected number of busy lines when someone calls?

My Ans: E(x) = 6 * p = ?

(c). Find the cumulative distribution function(cdf) for X.

?

(d).During the first two weeks in April, the firm experiences triple the number of calls it normally does. Find the expected number of busy lines during this time frame.

?

Answer #1

A business has six customer service telephone lines. Consider
the random variable x = number of lines in use at a randomly
selected time. Suppose that the probability distribution of x is as
follows. x 0 1 2 3 4 5 6
0.05 0.10. 0.17 0.41. 0.17 0.07 0.03
Calculate the mean value and standard deviation of x. (Round
your standard deviation to four decimal places.)
μx=
σx=
What is the probability that the number of lines in use is...

A business has six customer service telephone lines. Consider
the random variable x = number of lines in use at a
randomly selected time. Suppose that the probability distribution
of x is as follows.
x
0
1
2
3
4
5
6
p(x)
0.05
0.10
0.18
0.39
0.18
0.07
0.03
(a)
Calculate the mean value and standard deviation of x.
(Round your standard deviation to four decimal places.)
μx
=
σx
=
(b)
What is the probability that the number...

A mail-order computer software business has six telephone
lines. Let x denote the number of lines in use at a specified time.
The probability distribution of x is as follows:
X P(x)
0 0.11
1 0.17
2 0.20
3 0.25
4 0.15
5 0.08
6 0.04
Calculate the probability of:
(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...

6. A continuous random variable X has probability density
function
f(x) =
0 if x< 0
x/4 if 0 < or = x< 2
1/2 if 2 < or = x< 3
0 if x> or = 3
(a) Find P(X<1)
(b) Find P(X<2.5)
(c) Find the cumulative distribution function F(x) = P(X< or
= x). Be sure to define the function for all real numbers x. (Hint:
The cdf will involve four pieces, depending on an interval/range
for x....

A random variable X has the cumulative distribution function
(cdf) given by F(x) = (1 + e−x ) −1 , −∞ <
x < ∞.
(i) Find the probability density function (pdf) of X.
(ii) Roughly, take 10 points in the range of x (5 points below 0
and 5 points more than 0) and plot the pdf on these 10 points. Does
it look like the pdf is symmetric around 0?
(iii) Also, find the expected value of X.

X is a discrete random variable representing number of
conforming parts in a sample and has following probability mass
function
?(?) = { ?(5 − ?) if ? = 1, 2, 3, 4
0 otherwise
i) Find the value of constant ? and justify your answer
. ii) ( Determine the cumulative distribution function of X, (in
the form of piecewise function).
iii) Use the cumulative distribution function found in question
2 to determine the following:
a) ?(2 < ?...

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