Reggie

2020-11-01

The random variable X follows a normal distribution $?\left(20,102\right)$.
Find $F\in dP\left(?>30\right)$,

### Answer & Explanation

Brighton

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: $X\sim N\left(\mu =20,{\sigma }^{2}=102\right)$
Step 2
We need to compute $Pr\left(X\ge 30\right)$.
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
$Pr\left(X\ge 30\right)=Pr\left(Z\ge \frac{30-20}{10.1}\right)=Pr\left(Z\ge 0.9901\right)$
$=1-0.8389=0.1611$
$Pr\left(X\ge 30\right)=0.1611$

Jeffrey Jordon