Questions: A popcorn company finds that their 1 kg bags have a mean of 1,040 grams with a standard deviation of 25 grams. What is the z-score for a bag weighing 975 grams? Round your answer to the nearest tenth.

Solution Steps

We need to find the \( z \)-score for a bag of popcorn weighing 975 grams, given that the mean weight of the bags is 1040 grams with a standard deviation of 25 grams.

The formula for calculating the \( z \)-score is:

\[ z = \frac{X - \mu}{\sigma} \]

where:

• \( X \) is the value for which we are calculating the \( z \)-score (975 grams),
• \( \mu \) is the mean of the distribution (1040 grams),
• \( \sigma \) is the standard deviation of the distribution (25 grams).

Substitute the given values into the formula:

\[ z = \frac{975 - 1040}{25} \]

Perform the calculation:

\[ z = \frac{-65}{25} = -2.6 \]

Final Answer