The IQ scores are RVs (X) normally distributed with mean [tex] \mu=104 [/tex] and standard deviation [tex] \sigma =16 [/tex].
The probability [tex] P(X<76) [/tex] is calculated after converting the raw score to the standard score,
[tex] P(X<76)=P(\frac{X-\mu}{\sigma}<\frac{76-104}{16}) \\
P(X<76)=P(z<-1.75) \\
P(X<76)=\Phi(-1.75) [/tex].
Now use normal distribution table or technology,
[tex] P(X<76)=\Phi(-1.75) =0.0401 [/tex].
Thus, the number of people who would have I.Q.s below 76 out of 52,000 is
[tex] 0.0401*52000=2,085.2 [/tex].
Therefore, the approximate number is [tex] 2,083 [/tex].
