Respuesta :
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:
The length of a newborn girl whose length is at the 90th percentile is 51.5 centimeters.
What is a z-score?
The z-score is a numerical measurement used in statistics of the value's relationship to the mean of a group of values, measured in terms of standards from the mean.
Assume that lengths of newborn girls are normally distributed with a mean of 49.2 centimeters and a standard deviation of 1.8 centimeters.
The value of z for 90% is 1.2816.
Then the length of a newborn girl whose length is at the 90th percentile will be
[tex]\rm z = \dfrac{x - \mu}{\sigma}\\\\x = z\sigma + \mu\\\\x = 1.2816 \times 1.8 + 49.2\\\\x = 51.50[/tex]
More about the z-score link is given below.
https://brainly.com/question/15016913
