Let X \sim N(6,4).Find the probabilities P(5<X<7).

Annette Arroyo 2020-11-16 Answered

Let XN(6,4).Find the probabilities P(5<X<7).

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Expert Answer

casincal
Answered 2020-11-17 Author has 82 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(5<X<7) is computed as follows:
P(5<X<7)=P(X<7)P(x<5)
=P(Xμσ2<7μσ2)P(Xμσ2<5μσ2)
=P(Z<764)P(Z<564)
=P(Z<0.5)P(Z<0.5)
=P(Z<0.5)[1P(Z<0.5)]
=0.69146(10.69146)
=0.691460.30854=0.38292
Therefore,
P(5<X<7)=0.3829

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