### Understanding Normal Distributions in Temperature DataIn Paradise City, temperatures during June follow a nearly normal distribution pattern. This distribution has a mean (average) temperature of 80 degrees Fahrenheit and a standard deviation of 6 degrees Fahrenheit. In this context, the standard deviation is a measure of how much temperatures typically vary from the mean.#### Question:Which of the following temperatures would be considered unusual?- 72.8°F- 79.4°F- 65°F- 82.4°F- 82.4°FTo determine if a temperature is unusual, we need to consider how far it deviates from the mean in terms of standard deviation units (also known as Z-scores). Generally, values that are more than 2 standard deviations away from the mean are considered unusual. ***Example Calculation:***- Mean (μ) = 80°F- Standard Deviation (σ) = 6°FLet's calculate how far 65°F is from the mean:\[ \text{Z-score} = \frac{(X - \mu)}{\sigma} \]\[ \text{Z-score for 65°F} = \frac{(65 - 80)}{6} \]\[ \text{Z-score for 65°F} = \frac{-15}{6} \]\[ \text{Z-score for 65°F} = -2.5 \]A Z-score of -2.5 indicates that 65°F is 2.5 standard deviations below the mean. Since this is more than 2 standard deviations away from the mean, the temperature of 65°F would be considered unusual.Let's review each temperature to identify which is considered unusual:- 72.8°F -> Calculate its Z-score- 79.4°F -> Calculate its Z-score- 65°F -> Already calculated as unusual- 82.4°F -> Calculate its Z-score- 82.4°F -> Same as the previous 82.4°FYou can perform similar Z-score calculations to determine the usualness of the other temperatures. Generally, a Z-score greater than 2 or less than -2 indicates an unusual value.**Note:** The repeated value of 82.4°F seems to be a duplicate choice in the provided options. To ensure clarity, confirm that each option represents a distinct value when constructing your question set.

Normal distribution is a continuous distribution which has many real life applications. Normal curve…

Temperatures in June in the Paradise City are distributed nearly normally with mean 80 degrees and standard deviation 6 degrees F. Which of the following temperatures would be considered unusual? O 72.8 O 79.4 O 65 ) 82.4 O 82.4

Temperatures in June in the Paradise City are distributed nearly normally with mean 80 degrees and standard deviation 6 degrees F. Which of the following temperatures would be considered unusual? O 72.8 O 79.4 O 65 ) 82.4 O 82.4

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Question

### Understanding Normal Distributions in Temperature Data

In Paradise City, temperatures during June follow a nearly normal distribution pattern. This distribution has a mean (average) temperature of 80 degrees Fahrenheit and a standard deviation of 6 degrees Fahrenheit. In this context, the standard deviation is a measure of how much temperatures typically vary from the mean.

#### Question:
Which of the following temperatures would be considered unusual?

- 72.8°F
- 79.4°F
- 65°F
- 82.4°F
- 82.4°F

To determine if a temperature is unusual, we need to consider how far it deviates from the mean in terms of standard deviation units (also known as Z-scores). Generally, values that are more than 2 standard deviations away from the mean are considered unusual.

***Example Calculation:***
- Mean (μ) = 80°F
- Standard Deviation (σ) = 6°F

Let's calculate how far 65°F is from the mean:
\[ \text{Z-score} = \frac{(X - \mu)}{\sigma} \]
\[ \text{Z-score for 65°F} = \frac{(65 - 80)}{6} \]
\[ \text{Z-score for 65°F} = \frac{-15}{6} \]
\[ \text{Z-score for 65°F} = -2.5 \]

A Z-score of -2.5 indicates that 65°F is 2.5 standard deviations below the mean. Since this is more than 2 standard deviations away from the mean, the temperature of 65°F would be considered unusual.

Let's review each temperature to identify which is considered unusual:

- 72.8°F -> Calculate its Z-score
- 79.4°F -> Calculate its Z-score
- 65°F -> Already calculated as unusual
- 82.4°F -> Calculate its Z-score
- 82.4°F -> Same as the previous 82.4°F

You can perform similar Z-score calculations to determine the usualness of the other temperatures. Generally, a Z-score greater than 2 or less than -2 indicates an unusual value.

**Note:** The repeated value of 82.4°F seems to be a duplicate choice in the provided options. To ensure clarity, confirm that each option represents a distinct value when constructing your question set.

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