Tahmid Knox

2020-12-06

A population of values has a normal distribution with $\mu =13.7$ and $\sigma =22$.
You intend to draw a random sample of size $n=78$.
Find the probability that a single randomly selected value is less than 11.5.
$P\left(X<11.5\right)=$?

Szeteib

Expert

Step 1
From the provided information,
Mean $\left(\mu \right)=13.7$
Standard deviation $\left(\sigma \right)=22$
Let X be a random variable which represents the score.
$X\sim N\left(13.7,22\right)$
Sample size $\left(n\right)=78$
Step 2
The required probability that a single randomly selected value is less than 11.5
can be obtained as:
$P\left(X,11.5\right)=P\left(\frac{x-\mu }{\sigma }<\frac{11.5-13.7}{22}\right)$
$=P\left(Z<-0.1\right)=0.4602$ (Using standard normal table)
Thus, the required probability is 0.4602.

Jeffrey Jordon

Expert