Find the probability such that X x. How does this probability compare to your cl
ID: 3350488 • Letter: F
Question
Find the probability such that X x. How does this probability compare to your classmate’s calculation for X = x? In your own words explain what the difference is and what this probability means in the context of their situation.
Let's say the binomial probability is to see how probable is it that students in a statistics class will post their discussion posts by their due date, Saturday. It is binomial because the discussion posts will either be posted on time or not.
In my example, the sample size will be 8 discussion posts. N = 8
Probability of event interest, TT = 1
The number of events of interest, x = 4
The probability that 4 out of the sample of 8 discussion posts will be posted on time equals .0046 = .46% according to the CUMULATIVE tab on the binomial.xlsx workbook.
Binomial Probabilities Table
X
P(X)
P(<=X)
P(<X)
P(>X)
P(>=X)
0
0.4305
0.4305
0.0000
0.5695
1.0000
1
0.3826
0.8131
0.4305
0.1869
0.5695
2
0.1488
0.9619
0.8131
0.0381
0.1869
3
0.0331
0.9950
0.9619
0.0050
0.0381
4
0.0046
0.9996
0.9950
0.0004
0.0050
5
0.000408
0.999977
0.999568
2.34E-05
0.000432
6
2.27E-05
0.999999
0.999977
7.3E-07
2.34E-05
7
7.2E-07
1
0.999999
1E-08
7.3E-07
8
1E-08
1
1
0
Binomial Probabilities Table
X
P(X)
P(<=X)
P(<X)
P(>X)
P(>=X)
0
0.4305
0.4305
0.0000
0.5695
1.0000
1
0.3826
0.8131
0.4305
0.1869
0.5695
2
0.1488
0.9619
0.8131
0.0381
0.1869
3
0.0331
0.9950
0.9619
0.0050
0.0381
4
0.0046
0.9996
0.9950
0.0004
0.0050
5
0.000408
0.999977
0.999568
2.34E-05
0.000432
6
2.27E-05
0.999999
0.999977
7.3E-07
2.34E-05
7
7.2E-07
1
0.999999
1E-08
7.3E-07
8
1E-08
1
1
0
Explanation / Answer
1)
P(X = 4) = 0.0046
It means that the probability that 4 out of the sample of 8 discussion posts will be posted on time equals .0046 = .46%
P(X>= 4) = 0.0050
It means that the probability that 4 or more than 4 out of the sample of 8 discussion posts will be posted on time equals .0050 = 0.5 %
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