EXPLANATION
We have that the mean is μ= 55.8 and the standard deviation is σ = 7.8 inches
We can get the probability by first computing the z-score as follows:
a) For height < 37.7 inches --> x=37.7
[tex]z=\frac{x-u}{\sigma}=\frac{37.7-55.8}{7.8}=\frac{-18.1}{7.8}=-2.32[/tex]
Applying the z-score table:
[tex]P(x<37.7)=0.0102[/tex]
b) For height more than 58.3 inches x>58.3 ---> P(x>58.3) = 1- P(x<58.3)
Computing P(x<58.3):
[tex]z=\frac{58.3-55.8}{7.8}=\frac{2.5}{7.8}=0.3205[/tex]
Applying the z-score table:
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