Answer:
The percentile of Lucile is 15%.
Step-by-step explanation:
As per given data
Mean=μ=84
Standard Deviation=σ=6
Marks of Lucille=X=78
So the percentile for the normal distribution is given as
For this the Z value is calculated as
[tex]z=\frac{X-\mu}{\sigma}\\z=\frac{78-84}{6}\\z=\frac{-6}{6}\\z=-1[/tex]
For the Z value of -1, from the Z table the value of P is found as
P(X<78)=P(Z<-1)=0.1587=15.87%
So the percentile of Lucile is 15%.
