Answer: 2.28 %
Step-by-step explanation:
Given : Mean : [tex]\mu=\ 48[/tex]
Standard deviation :[tex]\sigma= 12[/tex]
The formula to calculate the z-score :-
[tex]z=\dfrac{x-\mu}{\sigma}[/tex]
For x = 72
[tex]z=\dfrac{72-48}{12}=2[/tex]
The p-value = [tex]P(2<z)=1-P(z<2)[/tex]
[tex]1-0.9772498=0.0227502\approx0.0228[/tex]
In percent, [tex]0.0228\times100=2.28\%[/tex]
Hence, the percentage of pediatricians work more than 72 h per week = 2.28 %
