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

rastafarral6

rastafarral6

Answered question

2021-11-09

If X is a normal random variable with parameters
μ=10
and
σ2=36
, compute P[X<20]

Answer & Explanation

Forneadil

Forneadil

Beginner2021-11-10Added 18 answers

Given that X is a mean-containing normal random variable μ=10 and variance σ2=36.
The following probability will be calculated using the knowledge that if XN(μ,σ2), then Z=XμσN(0,1), i.e; Z is a standard normal variable with Φ being its cdf, whose probabilities are calculable using the normal table.
P[X<20]=P[Xμσ<20106]
=P[Z<53]
=Φ(53)
=0.9522

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