Question

a child is 37.2 inches tall. the population of children of the same age and gender have a mean height of 39.2 inches with a standard deviation of 6.4 inches. another child is 38.9 inches tall. the population of children of the same age and gender as this child have a mean height of 40.5 inches with a standard deviation of 3.7 inches.
a) which child is taller?
(this is not a trick question...no statistics involved here)
child 2
o child 1
b) what is the z - score associated with the height of child 1?
round final answer to two decimal places.
enter an integer or decimal number more...
c) what is the z - score associated with the height of child 2?
round final answer to two decimal places.
d) which child is taller relative to their corresponding populations?
(now you have to use statistics)
o child 2
o child 1

Explanation:

Step1: Compare raw - heights for part a

Child 1 is 37.2 inches tall and child 2 is 38.9 inches tall. Since 38.9>37.2, child 2 is taller in terms of raw - height.

Step2: Calculate z - score for child 1 for part b

The formula for the z - score is $z=\frac{x-\mu}{\sigma}$, where $x$ is the value, $\mu$ is the mean, and $\sigma$ is the standard deviation. For child 1, $x = 37.2$, $\mu=39.2$, and $\sigma = 6.4$. Then $z_1=\frac{37.2 - 39.2}{6.4}=\frac{-2}{6.4}\approx - 0.31$.

Step3: Calculate z - score for child 2 for part c

For child 2, $x = 38.9$, $\mu = 40.5$, and $\sigma=3.7$. Then $z_2=\frac{38.9 - 40.5}{3.7}=\frac{-1.6}{3.7}\approx - 0.43$.

Step4: Compare z - scores for part d

The z - score of child 1 is approximately $-0.31$ and the z - score of child 2 is approximately $-0.43$. Since $-0.31>-0.43$, child 1 is taller relative to their corresponding population.

Answer:

a. child 2
b. - 0.31
c. - 0.43
d. child 1