91Ó°ÊÓ

Given in the question that the gestation periods of humans have a mean of $266$days and a standard deviation of $16$days. Let $y$denote the variable "gestation period" for humans. we have to find the standardized variable corresponding to $y$.

$y\text{'}s$standardized variable is determined as follows:

$$\begin{gathered} z=\frac{y-\mathrm{μ}}{\mathrm{σ}} \\ =\frac{y-266}{16} \end{gathered}$$

Given in the question that the gestation periods of humans have a mean of$266$days and a standard deviation of $16$days. Let $y$denote the variable "gestation period" for humans. we have to find the mean and standard deviation of the standardized variable .

The mean is computed as follows

$$\begin{gathered} {\mathrm{μ}}_{\mathrm{z}}=\frac{∑\frac{y_{\mathrm{i}}-\mathrm{μ}}{\mathrm{σ}}}{n} \\ =\frac{∑y_i-n\mathrm{μ}}{\mathrm{σ}n} \\ =\frac{n\mathrm{μ}-n\mathrm{μ}}{\mathrm{σ}n} \\ =0 \end{gathered}$$

The standard deviation is computed as follows

$$\begin{gathered} {\mathrm{σ}}_{\mathrm{Z}}=\sqrt{\frac{∑{\left(z_i-{\mathrm{μ}}_z\right)}^2}{n}} \\ =\frac{\mathrm{σ}}{\mathrm{σ}} \\ =1 \end{gathered}$$

Given in the question that the gestation periods of humans have a mean of $266$days and a standard deviation of $16$days. Let $y$denote the variable "gestation period" for humans. we have to find the $z$-scores for gestation periods of $227$days and $315$days.

score is calculated as

$$\begin{gathered} z_1=\frac{y_1-\mathrm{μ}}{\mathrm{σ}} \\ =\frac{227-266}{16} \\ ≈-2.44 \end{gathered}$$

$$\begin{gathered} z_2=\frac{y_2-\mathrm{μ}}{\mathrm{σ}} \\ =\frac{315-266}{16} \\ =3.06 \end{gathered}$$

Given in the question that the gestation periods of humans have a mean of $266$days and a standard deviation of $16$days. Let $y$denote the variable "gestation period" for humans. we have to Interpret your answers in part (c)

The first prisoner's $z$score revealed a standard deviation of $2.44$below the mean for prison time served.

The second prisoner's$z$score revealed a standard deviation of$3.06$ from the mean for prison time served.

Given in the question that the gestation periods of humans have a mean of $266$days and a standard deviation of $16$days. Let$y$denote the variable "gestation period" for humans. we have to construct a graph.