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.

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.
Transcript text: A popcorn company find that their 1 kg bags have a mean of $1,040 \mathrm{grams}$ 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.
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Solution

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Solution Steps

Step 1: Understand the Problem

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.

Step 2: Use the Z-score Formula

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).
Step 3: Substitute the Values

Substitute the given values into the formula:

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

Step 4: Calculate the Z-score

Perform the calculation:

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

Final Answer

The \( z \)-score for a bag weighing 975 grams is \(\boxed{-2.6}\).

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