Question

Heights of young adult women in the United States are approximately Normal with a mean of 64 inches and standard deviation 2.7 inches. What proportion of all young adult women in the United States are taller than 6 feet

Answer 1

Answer:

The proportion of all young adult women in the United States are taller than 6 feet(72 inches ) is  

   $P( X > 72) =0.0015233$

Step-by-step explanation:

From the question we are told that

   The mean is  $\mu = 64 \ inches$

    The standard deviation is  $\sigma = 2.7 \ inches$

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

       $P( X > 72) = P(\frac{X - \mu }{\sigma } > \frac{72 - 64 }{ 2.7 } )$

$\frac{X -\mu}{\sigma } = Z (The \ standardized \ value\ of \ X )$

       $P( X > 72) = P(Z > 2.963 )$

From the z-table

  The area under the normal  curve to the right corresponding to 2.963  is  

     $P(Z > 2.963 ) = 0.0015233$

=>   $P( X > 72) =0.0015233$