Question

suppose baby kittens weights have a mean of 12.5 and a standard deviation of 1.9. 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. $z = - 0.47$, $x=square$ round answer to two decimal places b. $z = 2.9$, $x=square$ roud answer to two decimal places

Explanation:

Step1: Rearrange the z - score formula

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

Step2: Calculate $x$ for part a

We know that $\mu = 12.5$, $\sigma=1.9$ and $z=- 0.47$. Substitute these values into $x = z\sigma+\mu$. So $x=-0.47\times1.9 + 12.5$. First, calculate $-0.47\times1.9=-0.893$. Then $x=-0.893 + 12.5=11.607\approx11.61$.

Step3: Calculate $x$ for part b

We know that $\mu = 12.5$, $\sigma = 1.9$ and $z = 2.9$. Substitute these values into $x=z\sigma+\mu$. So $x=2.9\times1.9+12.5$. First, calculate $2.9\times1.9 = 5.51$. Then $x=5.51+12.5 = 18.01$.

Answer:

a. $11.61$
b. $18.01$