A population of values has a normal distribution with μ=13.7 and σ=22. You intend to...

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

Answer is given below (on video)