Answer:
The proportion of all young adult women in the United States are taller than 6 feet(72 inches ) is
[tex]P( X > 72) =0.0015233[/tex]
Step-by-step explanation:
From the question we are told that
The mean is [tex]\mu = 64 \ inches[/tex]
The standard deviation is [tex]\sigma = 2.7 \ inches[/tex]
Generally 6 feet is equivalent to 6 * 12 = 72 inches
Generally the proportion of all young adult women in the United States are taller than 6 feet(72 inches ) is mathematically represented as
[tex]P( X > 72) = P(\frac{X - \mu }{\sigma } > \frac{72 - 64 }{ 2.7 } )[/tex]
[tex]\frac{X -\mu}{\sigma } = Z (The \ standardized \ value\ of \ X )[/tex]
[tex]P( X > 72) = P(Z > 2.963 )[/tex]
From the z-table
The area under the normal curve to the right corresponding to 2.963 is
[tex]P(Z > 2.963 ) = 0.0015233[/tex]
=> [tex]P( X > 72) =0.0015233[/tex]
