Five number summary: 4.33, 5.05, 5.44. 5.79, 6.81
mean pH: 5.43
standard deviation: 0.54
Given the proportion of observations are within 68%, 95%, and 99.7%, what is the acidity of the rainfall in pH value?
68% = mean ± 1 SD
95% = mean ± 2 SD
99.7% = mean ± 3 SD
To determine the acidity of the rainfall in pH value, we can use the mean pH and standard deviation provided, along with the concept of normal distribution.
1. First, let's recall what the proportions within different standard deviations represent in a normal distribution:
- Within one standard deviation of the mean (68%): This includes observations within one standard deviation above and below the mean.
- Within two standard deviations of the mean (95%): This includes observations within two standard deviations above and below the mean.
- Within three standard deviations of the mean (99.7%): This includes observations within three standard deviations above and below the mean.
2. Since we are given the mean pH as 5.43 and the standard deviation as 0.54, we can use this information to find the pH range for each proportion:
- Within 68%: This corresponds to one standard deviation above and below the mean. So, the pH range would be (5.43 - 0.54) to (5.43 + 0.54).
- Within 95%: This corresponds to two standard deviations above and below the mean. So, the pH range would be (5.43 - 2 * 0.54) to (5.43 + 2 * 0.54).
- Within 99.7%: This corresponds to three standard deviations above and below the mean. So, the pH range would be (5.43 - 3 * 0.54) to (5.43 + 3 * 0.54).
3. Now, let's calculate the pH range for each proportion:
- Within 68%: The pH range would be (4.35) to (6.51).
- Within 95%: The pH range would be (3.81) to (6.99).
- Within 99.7%: The pH range would be (3.27) to (7.53).
Therefore, based on the given data and proportions, the acidity of the rainfall in pH value would fall within the range of 4.35 to 6.51 for 68% of observations, 3.81 to 6.99 for 95% of observations, and 3.27 to 7.53 for 99.7% of observations.