Answer:
a) 89%; b) 68%
Step-by-step explanation:
We know that a mean [tex]\mu=166[/tex] and a standard deviation is [tex]\sigma=6.[/tex]
a) Notice that 148 and 184 are each exactly 3 standard deviation away from the mean:
[tex]\frac{148-166}{6}=-3\\ \frac{184-166}{6}=3\\[/tex]
So, we get that at least [tex](1-(\frac{1}{3} )^2)=89%[/tex] of the men has a height between 148 cm and 184 cm.
b) Notice that 160 and 172 are exactly 1 standard deviation away from the mean.
[tex]\frac{160-166}{6}=-1\\\\\frac{172-166}{6}=1[/tex]
By the empirical rule , 68% of the men has a height between 160 cm and 172 cm.
