Temperatures in June in the Paradise City are distributed nearly normally with mean 85 degrees and standard deviation 7 degrees F. Which of the following temperatures would be considered unusual? 71 O 76.6 O 78 O 76.6 O 94.1 Hint: Usual data z-scores have a value only between -2 and 2 inclusive
Inverse Normal Distribution
The method used for finding the corresponding z-critical value in a normal distribution using the known probability is said to be an inverse normal distribution. The inverse normal distribution is a continuous probability distribution with a family of two parameters.
Mean, Median, Mode
It is a descriptive summary of a data set. It can be defined by using some of the measures. The central tendencies do not provide information regarding individual data from the dataset. However, they give a summary of the data set. The central tendency or measure of central tendency is a central or typical value for a probability distribution.
Z-Scores
A z-score is a unit of measurement used in statistics to describe the position of a raw score in terms of its distance from the mean, measured with reference to standard deviation from the mean. Z-scores are useful in statistics because they allow comparison between two scores that belong to different normal distributions.
![### Temperature Analysis in Paradise City
**Problem Context:**
The temperatures in June in Paradise City are distributed nearly normally with a mean of 85 degrees and a standard deviation of 7 degrees Fahrenheit. The task is to determine which of the following temperatures would be considered unusual.
#### Multiple-Choice Question:
Which of the following temperatures would be considered unusual in Paradise City in June?
- [ ] 71
- [ ] 78
- [ ] 76.6
- [ ] 76.6
- [ ] 94.1
**Hint:** Usual data z-scores have a value only between -2 and 2 inclusive.
**Instructions:**
- Click the blue "Submit Question" button to finalize your choice.
#### Explanation:
To determine whether a temperature is unusual, we need to calculate its z-score. The z-score measures how many standard deviations an element is from the mean.
The formula for the z-score is:
\[ z = \frac{(X - \mu)}{\sigma} \]
Where:
- \(X\) is the value,
- \(\mu\) is the mean,
- \(\sigma\) is the standard deviation.
A z-score between -2 and 2 is considered usual.
**Example Calculation:**
Assuming \(X\) = 71:
\[ z = \frac{(71 - 85)}{7} \approx -2 \]
#### Answer Explanation:
- If the z-score of 71 is approximately -2, it lies at the boundary of what is considered usual (-2 to 2).
- Therefore, you need to perform similar calculations for the other temperatures to check their z-scores and determine whether they fall outside the -2 to 2 range.
**Submit Your Answer:**
Ensure to choose an option from the listed temperatures above and click "Submit Question."
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This transcribed and explained information aims to assist learners in understanding how to identify unusual data points in a normally distributed dataset using z-scores.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fdc9a01fb-7b2f-4b99-a4be-e5812986e7e1%2F49968d8e-7e3f-4d9f-97cc-2c1aee593049%2F6l6vz9u_processed.jpeg&w=3840&q=75)
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