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Sagot :
The average height is μ= 5.9ft and has a standard deviation of σ=0.2ft.
You have to determine the height (X) for the Z-score z=2
To determine this value, you have to use the formula of the standard deviation:
[tex]Z=\frac{X-\mu}{\sigma}[/tex]First, write the equation for X:
-Multiply both sides by sigma:
[tex]\begin{gathered} Z\sigma=\sigma\frac{X-\mu}{\sigma} \\ \\ Z\sigma=X-\mu \end{gathered}[/tex]-Add mu to both sides of it:
[tex]\begin{gathered} (Z\sigma)+\mu=X-\mu+\mu \\ X=(Z\sigma)+\mu \end{gathered}[/tex]Replace the expression obtained for X with the known values of z, sigma, and mu
[tex]\begin{gathered} X=2\cdot0.2+5.9 \\ X=\text{0}.4+5.9 \\ X=6.3 \end{gathered}[/tex]The height of a man that corresponds to z=2 is 6.3 ft
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