The annual precipitation for one city is normally distributed with a mean of 28 inches and a standard deviation of 3.4 inches. Fill in the blanks.
In 95% of the years, the precipitation in this city is between __________ and __________ inches.
Apply the 68-95-99.7 rule to this question.
A. 21.2, 34.8
B. 21.2, 34.6
C. 22.4, 34.6
D. 22.4, 34.8
is it C
No, it would be mean ± 2SD.
To find the range of precipitation that occurs in 95% of the years, we can apply the 68-95-99.7 rule, also known as the empirical rule or the three-sigma rule. According to this rule:
- Approximately 68% of the data falls within one standard deviation from the mean.
- Approximately 95% of the data falls within two standard deviations from the mean.
- Approximately 99.7% of the data falls within three standard deviations from the mean.
Given that the mean annual precipitation is 28 inches and the standard deviation is 3.4 inches, we can calculate the range:
- Two standard deviations below the mean: 28 - (2 * 3.4) = 21.2
- Two standard deviations above the mean: 28 + (2 * 3.4) = 34.8
Therefore, the precipitation in this city is between 21.2 and 34.8 inches in 95% of the years.
Based on the options provided, the correct answer is A. 21.2, 34.8 inches.