Question

z - scores: for human pregnancies, the population mean μ = 266 days and the standard deviation σ = 16 days. a shaded a normal curve graph for the proportion (or percentage) of humans whose pregnancies last less than 254 days. the figure has been drawn and shaded below.
x = 254
218 234 250 266 282 298 314
it happens to be that the area that is shaded below 254 is 22.66% or 0.2266. as probability notation that is written as p(x < 254)=0.2266.
calculate a z - score for the human gestation period of x = 254 days where μ = 266 days and σ = 16 days. enter the z - score rounded to 2 decimal places.
z=
remember that z=\frac{x - mu}{sigma}

Explanation:

Step1: Recall z - score 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 population mean, and $\sigma$ is the population standard deviation.

Step2: Substitute given values

We are given that $x = 254$, $\mu=266$, and $\sigma = 16$. Substitute these values into the formula: $z=\frac{254 - 266}{16}$.

Step3: Calculate the numerator

$254-266=-12$. So, $z=\frac{-12}{16}$.

Step4: Calculate the z - score

$\frac{-12}{16}=- 0.75$.

Answer:

$-0.75$