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Question
The mean and standard deviation of a binomial variate X are respectively 6 and 2. Find P(X = 3)
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Solution
X ~ B(n, p)
Given, Mean = 6
Standard deviation = 2
np = 6, `sqrt("npq")` = 2
npq = 4
`"npq"/"np"= 4/6`
q = `2/3`
p = 1 – q = `1/3`
npq = 4
`n" xx 1/3 xx 2/3` = 4
n = 18
P(X = 3) = `""^18"C"_3 (1/3)^3 (2/3)^15`
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