Let X \sim N(6,4).Find the probabilities P(X<3).

Anish Buchanan 2021-01-31 Answered

Let XN(6,4).Find the probabilities P(X<3).

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Expert Answer

davonliefI
Answered 2021-02-01 Author has 79 answers

Step 1
Introduction:
The normal probability is a type of continuous probability distribution that can take random values. The normal distribution is determined by the two parameters - the population mean (μ) and population variance (σ2). It is symmetric with respect to its mean.
Given information:
XN(6,4)
Therefore,
μ=6
σ2=4

Step 2
P(X<3) is computed as follows:
P(X<3)=P(Xμσ2<3μσ2)
=P(Z<364)
=P(Z<1.5)
=1P(Z<1.5)
=10.93319=0.06681
Therefore,
P(X<3)=0.0668

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