Reggie

2020-11-01

The random variable X follows a normal distribution $?(20,102)$ .

Find$F\in dP(?>30)$ ,

Find

Brighton

Skilled2020-11-02Added 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:$X\sim N(\mu =20,{\sigma}^{2}=102)$

Step 2

We need to compute$Pr(X\ge 30)$ .

The corresponding z-value needed to be computed is:

$Z=\frac{X-\mu}{\sigma}=\frac{30-20}{10.1}=0.9901$

Therefore, we get that

$Pr(X\ge 30)=Pr(Z\ge \frac{30-20}{10.1})=Pr(Z\ge 0.9901)$

$=1-0.8389=0.1611$

$Pr(X\ge 30)=0.1611$

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:

Step 2

We need to compute

The corresponding z-value needed to be computed is:

Therefore, we get that

Jeffrey Jordon

Expert2021-11-14Added 2605 answers

Answer is given below (on video)

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