Question

jenny runs a large animal shelter. the nguyen family adopted a puppy named rosie from the shelter. when rosie was adopted, she had been at the shelter for 39 days. at jennys shelter, the length of stay for puppies has a mean of 33 days and a standard deviation of 17 days.
(a) find the z-score of rosies length of stay at the shelter relative to the the lengths of stay for all the puppies at the shelter. round your answer to two decimal places.
$z = 0.22$
(b) fill in the blanks to interpret the z-score of rosies length of stay at the shelter. make sure to express your answer in terms of a positive number of standard deviations.
rosies length of stay was 0.22 standard deviations above the mean length of stay for all puppies at the shelter.

Explanation:

Step1: Recall z-score formula

The z-score formula is $z = \frac{x - \mu}{\sigma}$, where $x$ is the observed value, $\mu$ is the population mean, and $\sigma$ is the population standard deviation.

Step2: Plug in given values

Substitute $x=39$, $\mu=33$, $\sigma=17$ into the formula:
$z = \frac{39 - 33}{17} = \frac{6}{17} \approx 0.35$

Step3: Interpret the z-score

A positive z-score means the observed value is above the mean.

Answer:

(a) $z = 0.35$
(b) Rosie's length of stay was 0.35 standard deviations above the mean length of stay for all puppies at the shelter.