Answer: 16
Step-by-step explanation:
Given : Mean : [tex]\mu=100[/tex]
Standard deviation : [tex]\sigma =15[/tex]
The value of z-score is given by :-
[tex]z=\dfrac{x-\mu}{\sigma}[/tex]
For x= 115
[tex]z=\dfrac{115-100}{15}=1[/tex]
The p-value : [tex]P(z>1)=1-P(z<1)=1- 0.8413447=0.1586553[/tex]
Now, the number of people smarter than Many is given by :_
[tex]100\times0.1586553=15.86553\approx16[/tex]
Hence, there are 16 members smarter than Mandy.
