weights of four - year - olds are normally distributed, with a mean of 40 pounds and a standard deviation of…

weights of four - year - olds are normally distributed, with a mean of 40 pounds and a standard deviation of 1.3 pounds. at her four - year checkup, hannahs weight measures in the 90th percentile. how much does hannah weigh? find the z - table here. 38.3 pounds 37.5 pounds 41.7 pounds 42.3 pounds

weights of four - year - olds are normally distributed, with a mean of 40 pounds and a standard deviation of 1.3 pounds. at her four - year checkup, hannahs weight measures in the 90th percentile. how much does hannah weigh? find the z - table here. 38.3 pounds 37.5 pounds 41.7 pounds 42.3 pounds

Answer

Answer:

C. 41.7 pounds

Explanation:

Step1: Find the z - score

Look up the z - score for the 90th percentile in the z - table. The z - score corresponding to the 90th percentile is approximately $z = 1.28$.

Step2: Use the z - score formula

The z - score formula is $z=\frac{x-\mu}{\sigma}$, where $x$ is the value we want to find, $\mu$ is the mean, and $\sigma$ is the standard deviation. We know $\mu = 40$, $\sigma=1.3$, and $z = 1.28$. Rearranging the formula for $x$ gives $x=\mu + z\sigma$.

Step3: Calculate Hannah's weight

Substitute the values into the formula: $x=40+1.28\times1.3=40 + 1.664\approx41.7$ pounds.