Answer:
Number of girls shorter than [tex]60[/tex] inches are [tex]301[/tex].
Step-by-step explanation:
Given: The heights of the population of girls in an Arlington, NY school follows a normal distribution.
Mean[tex]=63[/tex]
Standard deviation[tex]=2[/tex]
Total number of girls[tex]=450[/tex]
Now using the formula,
Standard normal variant, [tex]z=\frac{x-mean}{standard deviation}[/tex]
Now, substitute the values and replace [tex]x[/tex] by [tex]60[/tex]
So. [tex]z=\frac{60-63}{2}[/tex]
[tex]z=-\frac{3}{2}[/tex] or [tex]-1.5[/tex]
Now, probability of girls shorter than [tex]60[/tex] inches
[tex]p(z>-1.5)=0.668[/tex] look up the value in the normal distribution table
Therefore, number of girls shorter than [tex]60[/tex] inches
[tex]=0.668[/tex]×[tex]450[/tex]
[tex]=301[/tex]
