Fractions and Decimals

Discrete Mathematics

Differential Equations

Solved on Nov 16, 2023

A patient takes $\$7\$ days to recover from a surgical procedure with a mean recovery time of$ \ $4.9\$ days and a standard deviation of$ \ $2.1\$ days. Find the patient's$ z$-score. (Round to two decimal places.)

STEP 1

Assumptions1. The recovery time from the surgical procedure is normally distributed. . The mean recovery time is4.9 days.
3. The standard deviation of the recovery time is.1 days.
4. We are asked to find the $z$ -score for a patient who takes7 days to recover.

STEP 2

The formula for calculating a $z$ -score is $z = \frac{X - \mu}{\sigma}$ where $X$ is the value from the dataset (in this case, the recovery time of the patient), $\mu$ is the mean of the dataset, and $\sigma$ is the standard deviation of the dataset.

STEP 3

Now, plug in the given values for $X$ , $\mu$ , and $\sigma$ to calculate the $z$ -score.
$z = \frac{7 -.9}{2.1}$

STEP 4

First, calculate the difference between $X$ and $\mu$ .
$7 -4.9 =2.1$ So, the $z$ -score becomes $z = \frac{2.1}{2.1}$

STEP 5

Finally, calculate the $z$ -score.
$z = \frac{2.1}{2.1} =1$ So, the $z$ -score for a patient who takes7 days to recover is1.00 (rounded to two decimal places).

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