In a cooking contest, the mean score for appearance was 21, with a standard deviation of 2.6. One of the contestants received a score of 25. Convert this score to a z score and tell if it is "usual" or "unusual."

Answer 1

To convert a score to a z-score, you can use the following formula:

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

where:

• \(X\) is the score,
• \(\mu\) is the mean,
• \(\sigma\) is the standard deviation.

In this case:

• \(X = 25\)
• \(\mu = 21\)
• \(\sigma = 2.6\)

Now, plug in the values:

\[ z = \frac{(25 - 21)}{2.6} = \frac{4}{2.6} \approx 1.5385 \]

The z-score is approximately 1.54.

To determine if this score is "usual" or "unusual," we typically consider a z-score greater than 2 or less than -2 as unusual. Since 1.54 is within the range of -2 to +2, the score of 25 is considered "usual."