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

heights of four - year - olds are normally distributed, with a mean of 40 inches and a standard deviation of 3 inches. at his four - year checkup, marlons height is measured as taller than 70% of boys his age. how tall is marlon? find the z - table here. 38.4 inches 41.6 inches 42.5 inches 43.8 inches

heights of four - year - olds are normally distributed, with a mean of 40 inches and a standard deviation of 3 inches. at his four - year checkup, marlons height is measured as taller than 70% of boys his age. how tall is marlon? find the z - table here. 38.4 inches 41.6 inches 42.5 inches 43.8 inches

Answer

Explanation:

Step1: Find the z - score

We know that Marlon's height is taller than 70% of boys his age. Looking up the value in the standard normal (z -) table, the z - score corresponding to a cumulative probability of 0.70 is approximately $z = 0.52$.

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 that $\mu = 40$ inches, $\sigma= 3$ inches and $z = 0.52$. Rearranging the formula for $x$ gives $x=\mu + z\sigma$.

Step3: Calculate Marlon's height

Substitute the values into the formula: $x = 40+0.52\times3=40 + 1.56=41.56\approx41.6$ inches.

Answer:

41.6 inches