Assume that lengths of newborn girls are normally distributed with a mean of 49.2 centimeters and a standard deviation of 1.8 centimeters. what is the length of a newborn girl whose length is at the 90th percentile?

We have been given that lengths of newborn girls are normally distributed with a mean of 49.2 centimeters and a standard deviation of 1.8 centimeters.

We need to find the length of a newborn girl whose length is at the 90th percentile.

We know that 90th percentile corresponds to a z score of

Our last step is to solve this equation for x.

Therefore, length of the newborn girl is 51.5 centimeters.

Therefore, if we assume that length of the newborn girl is x, we can express an equation in x using the formula for z score:

use the power rule  

( a b ) n = a n b n

to distribute the exponent.

apply the product rule to  

3 x 2 y 3 . ( 3 x 2 ) 2 ( y 3 ) 2

apply the product rule to  

3 x 2 . 3 2 ( x 2 ) 2 ( y 3 ) 2

raise  

3

to the power of  

2 . 9 ( x 2 ) 2 ( y 3 ) 2 multiply the exponents in   ( x 2 ) 2

.

apply the power rule and multiply exponents,  

( a m ) n = a m n . 9 x 2 ⋅ 2 ( y 3 ) 2

multiply  

2   by   2 . 9 x 4 ( y 3 ) 2

multiply the exponents in  

( y 3 ) 2 .

apply the power rule and multiply exponents,  

( a m ) n = a m n . 9 x 4 y 3

⋅

2

multiply  

3   by   2 . 9 x 4 y 6

step-by-step explanation: