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Answer :
Final answer:
Temperatures that deviate more than three standard deviations from the mean would be considered unusual in a normal distribution. Based on the given mean and standard deviation, the temperatures of 65 degrees F and 86 degrees F would be considered unusual.
Explanation:
To determine which temperatures would be considered unusual, we can use the concept of standard deviation. In a normal distribution, approximately 68% of the data falls within one standard deviation of the mean, approximately 95% falls within two standard deviations, and approximately 99.7% falls within three standard deviations.
In this case, the standard deviation is 5 degrees F. So, temperatures that deviate more than three standard deviations from the mean would be considered unusual.
Let's calculate the z-scores for the given temperatures:
- A) 73 degrees F
Z-score = (73 - 77) / 5 = -0.8 - B) 80 degrees F
Z-score = (80 - 77) / 5 = 0.6 - C) 69 degrees F
Z-score = (69 - 77) / 5 = -1.6 - D) 65 degrees F
Z-score = (65 - 77) / 5 = -2.4 - E) 86 degrees F
Z-score = (86 - 77) / 5 = 1.8
Based on the z-scores, temperatures with a z-score greater than 3 or less than -3 would be considered unusual. Therefore, the temperatures of 65 degrees F and 86 degrees F would be considered unusual in this case.
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