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

Pearl Carney

Pearl Carney

Answered question

2021-11-08

If X is a normal random variable with parameters
μ=10
and
σ2=36
, compute P[X<8]

Answer & Explanation

Alfonso Miller

Alfonso Miller

Beginner2021-11-09Added 20 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<8]=P[Xμσ<8106]
=P[Z<13]
=Φ(13)
=0.3694

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