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

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

`P( X > 72) =0.0015233`

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((X - \mu )/(\sigma ) > (72 - 64 )/( 2.7 ) )`

`(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`