Question

for this application problem, assume that and that. compute these z - scores for these two classifications: option a: someone would be classified with \dwarfism\ if their height is less than 147cm. using your z - scores, determine the proportion of people in the full population (not the sample!) that would fit into the aforementioned classifications.

Explanation:

Step1: Recall z - score formula

The z - score formula is $z=\frac{x-\mu}{\sigma}$, where $x$ is the value from the data set, $\mu$ is the mean and $\sigma$ is the standard deviation. But the values of $\mu$ and $\sigma$ are not given in the problem statement. Let's assume $\mu$ and $\sigma$ are known values. For Option A, $x = 147$.

Step2: Calculate z - score for Option A

$z_A=\frac{147-\mu}{\sigma}$
To find the proportion of people in the full population that would fit into the classification, we use the standard normal distribution table (Z - table). The proportion $P(Z < z_A)$ can be found from the Z - table.

However, since $\mu$ and $\sigma$ are not given in the problem, we cannot calculate a numerical value for the z - score and proportion. If we assume $\mu$ and $\sigma$ are known, we would first calculate the z - score as above and then look up the value in the standard normal distribution table.

Answer:

We cannot calculate a numerical answer as the values of $\mu$ and $\sigma$ are not provided. If $\mu$ and $\sigma$ were known, the z - score for Option A would be $z_A=\frac{147 - \mu}{\sigma}$ and the proportion of the population with height less than 147cm would be $P(Z