Question

the weights of boxes of candies produced in a factory are normally distributed with a mean weight of 16 oz and a standard deviation of 1 oz. what is the weight of a box of candies with a z - score of 2?
16 oz
18 oz
20 oz
22 oz

Explanation:

Step1: Recall z - score formula

The z - score formula is $z=\frac{x-\mu}{\sigma}$, where $z$ is the z - score, $x$ is the value from the data set, $\mu$ is the mean, and $\sigma$ is the standard deviation. We need to solve for $x$.

Step2: Rearrange the formula for $x$

Starting with $z=\frac{x - \mu}{\sigma}$, we can multiply both sides by $\sigma$: $z\sigma=x-\mu$. Then add $\mu$ to both sides to get $x=\mu + z\sigma$.

Step3: Substitute given values

We are given that $\mu = 16$ oz, $z = 2$, and $\sigma=1$ oz. Substituting these values into the formula $x=\mu + z\sigma$, we have $x=16+2\times1$.

Step4: Calculate the value of $x$

$x=16 + 2=18$ oz.

Answer:

18 oz