the weights for 12 - month - old males are normally distributed with a mean of 22.6 pounds and a standard…

the weights for 12 - month - old males are normally distributed with a mean of 22.6 pounds and a standard deviation of 3.0 pounds. use the given table to find the percentage of 12 - month - old males who weigh more than 23.8 pounds. click the icon to view the table of z - scores and percentiles. % of 12 - month - old males weigh more than 23.8 pounds. (round to two decimal places as needed.)

the weights for 12 - month - old males are normally distributed with a mean of 22.6 pounds and a standard deviation of 3.0 pounds. use the given table to find the percentage of 12 - month - old males who weigh more than 23.8 pounds. click the icon to view the table of z - scores and percentiles. % of 12 - month - old males weigh more than 23.8 pounds. (round to two decimal places as needed.)

Answer

Explanation:

Step1: Calculate the z - score

The z - score formula is $z=\frac{x-\mu}{\sigma}$, where $x = 23.8$, $\mu=22.6$, and $\sigma = 3.0$. $z=\frac{23.8 - 22.6}{3.0}=\frac{1.2}{3.0}=0.4$

Step2: Find the percentile for the z - score

Looking up the z - score of 0.4 in the z - score table, we find the percentile is approximately 0.6554. This is the proportion of data less than $x = 23.8$.

Step3: Calculate the proportion of data greater than 23.8

The proportion of data greater than 23.8 is $1 - 0.6554=0.3446$.

Step4: Convert to percentage

To convert the proportion to a percentage, we multiply by 100. So the percentage is $0.3446\times100 = 34.46%$

Answer:

34.46%