Mandy has an IQ of 115. We know that the mean () IQ is 100 with a standard deviation of 15. There are 100 people in Mandy’s Alcoholics Anonymous meeting. Taken at random, how many members are smarter than Mandy

Answer: 16Step-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.