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 [tex]z=\frac{x-\mu }{\sigma }\Rightarrow 1.2816=\frac{x-49.2 }{1.8}[/tex]Our last step is to solve this equation for x.[tex]x-49.2=1.2816\times 1.8\Rightarrow x=49.2+2.30688\Rightarrow x=51.50688[/tex]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: