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jwoody5495
12.08.2020 •
Mathematics
In a binomial distribution, n = 8 and π=0.36. Find the probabilities of the following events. (Round your answers to 4 decimal places.)
a. x=5
b. x <= 5
c. x>=6
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Ответ:
P(x ≤ 5 ) = 0.9707
P ( x ≥ 6) = 0.0293
Step-by-step explanation:
The probability of a binomial mass distribution can be expressed with the formula:
where;
n = 8 and π = 0.36
For x = 5
The probability![\mathtt{P(X=5) =(\dfrac{8!}{5!(8-5)!} ) \ 0.36^5 \ (1-0.36)^{8-5}}](/tpl/images/0718/9703/42c4d.png)
b. x ≤ 5
The probability of P ( x ≤ 5)![\mathtt{P(x \leq 5) = P(x = 0)+ P(x = 1)+ P(x = 2)+ P(x = 3)+ P(x = 4)+ P(x = 5})](/tpl/images/0718/9703/46af9.png)
P(x ≤ 5 ) = 0.0281+0.1267+0.2494+0.2805+0.1972+0.0888
P(x ≤ 5 ) = 0.9707
c. x ≥ 6
The probability of P ( x ≥ 6) = 1 - P( x ≤ 5 )
P ( x ≥ 6) = 1 - 0.9707
P ( x ≥ 6) = 0.0293
Ответ: