Question

z - scores: in notes 5.1, exercise 4 at the bottom of the page, we shaded a normal curve graph for the proportion (or percentage) of elephants whose pregnancies last less than 501 days. the figure has been redrawn and shaded below. the notes say that the area that is shaded below 501 is 22.66% or 0.2266. as probability notation that is written as p(x < 501)=0.2266. calculate a z - score for the elephant gestation period of x = 501 days where μ = 525 days and σ = 32 days. enter the z - score rounded to 2 decimal places. remember that z=\frac{x - mu}{sigma}

Explanation:

Step1: Identify the formula

The formula for the z - score 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.

Step2: Substitute the given values

We are given that $x = 501$, $\mu=525$, and $\sigma = 32$. Substitute these values into the formula: $z=\frac{501 - 525}{32}$.

Step3: Calculate the numerator

$501-525=- 24$. So, $z=\frac{-24}{32}$.

Step4: Calculate the z - score

$\frac{-24}{32}=-0.75$.

Answer:

$-0.75$