If X is a normal random variable with parameters \mu=10 and PS

verskalksv

verskalksv

Answered question

2021-11-06

If X is a normal random variable with parameters
μ=10
and
σ2=36
, compute P[X>5]

Answer & Explanation

Todd Williams

Todd Williams

Beginner2021-11-07Added 18 answers

Given X is a normal random variable with mean μ=10 and variance σ2=36.
To compute the following probabilities, we will make use of the fact that if XN(μ,σ2), then Z=XμσN(0,1), i.e; Z is a standard normal variable with Φ being its cdf, whose proabilities can be computed using the standard normal table.
P[x>5]=P[xμσ>5106]
=P[Z>56]
=1Φ(56)
=1-0.2023
=0.7977

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