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Question
If X ∼ N (4,25), then find P(x ≤ 4)
Solution
Given X ∼ N (4,25),
μ = 4, `sigma^2` = 25 `therefore sigma` = 5
Let Z = `(x - μ)/sigma`
then Z ∼ N (0,1)
P(X ≤ 4) = P `((x - μ)/sigma ≤ (4 - 4)/5)`
= P (Z ≤ 0)
P(X ≤ 4) = 0.5
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Solution:
Here, n = 4
p = probability of defective device = 10% = `10/100 = square`
∴ q = 1 - p = 1 - 0.1 = `square`
X ∼ B(4, 0.1)
`P(X=x)=""^n"C"_x p^x q^(n-x)= ""^4"C"_x (0.1)^x (0.9)^(4 - x)`
P[At most one defective device] = P[X ≤ 1]
= P[X=0] + P[X=1]
= `square+square`
∴ P[X ≤ 1] = `square`
