91Ó°ÊÓ

Sketch the normal curve having the parameters:

Mean $\mathrm{μ}=−1$

Standard deviation$\mathrm{σ}=2$

The probability distribution curve of a normal random variable is called a normal curve.

It's a representation of a normal distribution in graphical form.

If $X$is a continuous random variable with mean $\mathrm{μ}$and standard deviation $\mathrm{σ}$, then a normal curve with random variable localid="1650897073505" $X$has the following equation:

localid="1650897079262" $f\left(x\right)=\frac{1}{\mathrm{σ}\sqrt{2\mathrm{π}}}{e}^{\frac{−(x−\mathrm{μ}{)}^2}{2{\mathrm{σ}}^2}};−\mathrm{∞}<x<\mathrm{∞},−\mathrm{∞}<\mathrm{μ}<\mathrm{∞},\mathrm{σ}>0.$

Furthermore, a normal curve with random variable localid="1650897086659" $Z$has the following equation:

localid="1650897092286" $f\left(z\right)=\frac{1}{\sqrt{2\mathrm{π}}}{e}^{\frac{−z^2}{2}}$

localid="1650897100801" $Z$has a mean of localid="1650897108373" $0$and a standard deviation of localid="1650897115084" $1$, correspondingly.

The population mean localid="1650897121663" $\mathrm{μ}$and the population standard deviation localid="1650897128400" $\mathrm{σ}$are two population metrics that are commonly included in a normal curve.

The bell-shaped normal distribution with localid="1650897134454" $\mathrm{μ}=-1$and localid="1650897140033" $\mathrm{σ}=2$depicts the area under the normal distribution curve.

Arealocalid="1650897146320" $(probability)=0.3085$

Sketch the normal curve having the parameters:

Mean$\mathrm{μ}=3$

Standard deviation$\mathrm{σ}=2$

The probability distribution curve of a normal random variable is called a normal curve. It's a representation of a normal distribution in graphical form.

If $X$is a continuous random variable with mean $\mathrm{μ}$and standard deviation $\mathrm{σ}$, then a normal curve with random variable $X$has the following equation:

$f\left(x\right)=\frac{1}{\mathrm{σ}\sqrt{2\mathrm{π}}}{e}^{\frac{-(x-\mathrm{μ}{)}^2}{2{\mathrm{σ}}^2}};-∞<x<∞,-∞<\mathrm{μ}<∞,\mathrm{σ}>0$

Furthermore, a normal curve with random variable $Z$has the following equation:

$f\left(z\right)=\frac{1}{\sqrt{2\mathrm{Ï€}}}{e}^{\frac{-z^2}{2}}$

$Z$has a mean of $0$and a standard deviation of $1$, correspondingly.

The population mean $\mathrm{μ}$and the population standard deviation $\mathrm{σ}$are two population metrics that are commonly included in a normal curve.

The bell-shaped normal distribution with $\mathrm{μ}=3$and $\mathrm{σ}=2$depicts the area under the normal distribution curve.

Area (probability)$=0.9332$

Sketch the normal curve having the parameters:

Mean$\mathrm{μ}=−1$

Standard deviation$\mathrm{σ}=0.5$

The probability distribution curve of a normal random variable is called a normal curve. It's a representation of a normal distribution in graphical form.

If $X$is a continuous random variable with mean $\mathrm{μ}$and standard deviation $\mathrm{σ}$, then a normal curve with random variable $X$has the following equation:

$f\left(x\right)=\frac{1}{\mathrm{σ}\sqrt{2\mathrm{π}}}{e}^{\frac{-(x-\mathrm{μ}{)}^2}{2{\mathrm{σ}}^2}};-∞<x<∞,-∞<\mathrm{μ}<∞,\mathrm{σ}>0$

Furthermore, a normal curve with random variable $Z$has the following equation:

$f\left(z\right)=\frac{1}{\sqrt{2\mathrm{Ï€}}}{e}^{\frac{-z^2}{2}}$

$Z$has a mean of $0$and a standard deviation of $1$, correspondingly.

The population mean $\mathrm{μ}$and the population standard deviation $\mathrm{σ}$are two population metrics that are commonly included in a normal curve.

The bell-shaped normal distribution with $\mathrm{μ}=-1$and $\mathrm{σ}=0.5$depicts the area under the normal distribution curve.

Area (probability)$=0.0228$