Question

Assume the random variable x is normally distributed with mean

mu equals 50μ=50

and standard deviation

sigma equals 7σ=7.

Find the indicated probability.

Upper P left parenthesis x greater than 35 right parenthesisP(x>35)

Answer 1

Here, μ = 50, σ = 7 and x = 35. We need to compute P(X >= 35). The corresponding z-value is calculated using Central Limit Theorem

z = (x - μ)/σ
z = (35 - 50)/7 = -2.14

Therefore,
P(X >= 35) = P(z <= (35 - 50)/7)
= P(z >= -2.14)
= 1 - 0.0162
= 0.9838