Question

suppose baby kittens weights have a mean of 11.4 and a standard deviation of 2.5. the z - score tells you how many standard deviations above the average (if z - score is positive) or below the average (if z - score is negative) any particular baby kittens weight is. find the baby kitten weight that corresponds to the following z - scores. use the formula $z=\frac{x - mu}{sigma}$ where $mu$ is the mean, $sigma$ is the standard deviation, and $x$ is the baby kitten weight. a. $z = - 0.98$, $x=$ round answer to two decimal places enter an integer or decimal number more.. b. $z = 0.96$, $x=$ roud answer to two decimal places

Explanation:

Step1: Rearrange the z - score formula

Given $z=\frac{x - \mu}{\sigma}$, we can solve for $x$: $x=\mu+z\sigma$.

Step2: Calculate $x$ for part a

We know that $\mu = 11.4$, $\sigma=2.5$ and $z=- 0.98$. Substitute these values into $x=\mu+z\sigma$:
$x = 11.4+(-0.98)\times2.5=11.4 - 2.45=8.95$

Step3: Calculate $x$ for part b

We know that $\mu = 11.4$, $\sigma = 2.5$ and $z = 0.96$. Substitute these values into $x=\mu+z\sigma$:
$x=11.4 + 0.96\times2.5=11.4+2.4 = 13.80$

Answer:

a. $8.95$
b. $13.80$