3) A Conference Center usually has five clients per day. Over the years the mana
ID: 3160380 • Letter: 3
Question
3) A Conference Center usually has five clients per day. Over the years the management has recorded the number of cancellations and used the data to estimate the probability of 0 through 5 cancellations per day. In the table below X = number of cancellations per day and P(X) = the probability of x cancellations.
X
0
1
2
3
4
5
P(X)
0.205
0.410
0.328
0.051
0.005
0.001
a) Compute the expected number of cancellations per day (to the nearest 2nd decimal)
b) Compute the standard deviation for the number of cancellations (to the nearest 2nd decimal).
c) What is the probability that there will be 3 or more cancellations in a day?
d) What is the probability that there will be 2 or fewer cancellations in a day?
X
0
1
2
3
4
5
P(X)
0.205
0.410
0.328
0.051
0.005
0.001
Explanation / Answer
3.
a.
f= 1
fx = 1.244
Mean = fx / f = 1.244
b.
Mean square = f x^2 / f = 2.286
Varriance = (Mean square) - (Mean)^2
Varriance = f x^2 - Mean^2 = 0.738
Stadard Dev= Var = 0.859
c.
P(X>=3) = P(X=3) + P(X=4) + P(X=5) = 0.051+0.005+0.001 = 0.057
d.
P(X<=2) = P(X=0) + P(X=1)+P(X=2) = 0.205 + 0.410 + 0.328 = 0.943
Values ( X ) Frequency(f) fx ( X^2) f x^2 0 0.205 0 0 0 1 0.41 0.41 1 0.41 2 0.328 0.656 4 1.312 3 0.051 0.153 9 0.459 4 0.005 0.02 16 0.08 5 0.001 0.005 25 0.025Related Questions
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