Let X be the height measurement of ten years children in a country of united states.
Then,
[tex]X\approx N(55.8,7.8)[/tex]
To find
[tex]P(X<37.7)[/tex]
Using the definition
[tex]Z=\frac{X-\mu}{\sigma}[/tex]
[tex]P(X<37.7)=0.0102[/tex]
Hence, the probability that a randomly chosen child has a height less than 37.7 inches is 0.0102.
Now,
[tex]P(X>58.3)=0.3743[/tex]
Hence, the probability that a randomly chosen child has a height more than 58.3 inches is 0.3743.
