Question
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."
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Answered by
GPT-4o mini
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."
\[
z = \frac{(X - \mu)}{\sigma}
\]
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."
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