Question

Assume that x has a normal distribution with the specified mean and standard deviation. Find the indicated probability. (Enter a number. Round your answer to four decimal places.)

μ = 18; σ = 3.6

P(x ≥ 30) =

Answer 1

We have given that x follows the normal distribution with mean μ = 18 and standard deviation σ = 3.6

We want to find P(x ≥ 30)

Use the standardisation for solving this problem,

P (x ≥ 30) = P {(X – μ) / σ ≥ (30 - 18)/3.6}

                               = P (z ≥ 3.333)

                              = 1 - P (z < 3.333)

                              = 1 – 0.9996….. (From the standard normal table)

                              = 0.0004

P(x ≥ 30) = 0.0004.