the weights of a pack of chewing gum for a certain brand have a mean of 47.1 grams and a standard deviation…

Answer:

D. 54.6 grams

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 want to find $x$.

Step2: Rearrange the formula for $x$

Rearranging $z=\frac{x - \mu}{\sigma}$ gives $x=\mu+z\sigma$.

Step3: Substitute given values

We are given that $\mu = 47.1$, $z = 3.11$, and $\sigma=2.4$. Substituting these values into the formula $x=\mu + z\sigma$, we get $x=47.1+3.11\times2.4$.

Step4: Calculate the value of $x$

First, calculate $3.11\times2.4 = 7.464$. Then, $x=47.1 + 7.464=54.564\approx54.6$ grams.