Answer: 95.45 %
Step-by-step explanation:
Given : The distribution is bell shaped , then the distribution must be normal distribution.
Mean : [tex]\mu=\ 16[/tex]
Standard deviation :[tex]\sigma= 1.5[/tex]
The formula to calculate the z-score :-
[tex]z=\dfrac{x-\mu}{\sigma}[/tex]
For x = 13
[tex]z=\dfrac{13-16}{1.5}=-2[/tex]
For x = 19
[tex]z=\dfrac{19-16}{1.5}=2[/tex]
The p-value = [tex]P(-2<z<2)=P(z<2)-P(z<-2)[/tex]
[tex]0.9772498-0.0227501=0.9544997\approx0.9545[/tex]
In percent, [tex]0.9545\times100=95.45\%[/tex]
Hence, the percentage of data lie between 13 and 19 = 95.45 %
