The random variable X follows a normal distribution ?(20, 102). Find Find P(? > 30 ),

Reggie 2020-11-01 Answered
The random variable X follows a normal distribution ?(20,102).
Find FdP(?>30),
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Brighton
Answered 2020-11-02 Author has 103 answers
Step 1
Normal probability is a type of continuous probability distribution that can take random values on the whole real line. The main properties of the normal distribution are:
-It is continuous (and as a consequence, the probability of getting any single, specific outcome is zero)
-It has a "bell shaped" distribution (and that is where the "Bell-Curve" name comes along)
-The normal distribution is determined by two parameters: the population mean and population standard deviation
-It is symmetric with respect to its mean.
Given : The random variable X follows a normal distribution .
Notation: XN(μ=20,σ2=102)
Step 2
We need to compute Pr(X30).
The corresponding z-value needed to be computed is:
Z=Xμσ=302010.1=0.9901
Therefore, we get that
Pr(X30)=Pr(Z302010.1)=Pr(Z0.9901)
=10.8389=0.1611
Pr(X30)=0.1611
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Jeffrey Jordon
Answered 2021-11-14 Author has 2064 answers

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