The typical American generates about 3.8 pounds of solid trash per day with a standard deviation of 1.5 pounds. Assuming that the histogram for trash produced per day is approx. bell shaped, between what two values will 95% of the observation fall???
Thanks
95% = mean ± 1.96 SD
0.8 lbs and 6.8 lbs
To find the range in which 95% of the observations will fall, we can use the concept of the empirical rule, also known as the 68-95-99.7 rule. According to this rule, in a bell-shaped distribution:
- Approximately 68% of the observations will fall within one standard deviation of the mean.
- Approximately 95% of the observations will fall within two standard deviations of the mean.
- Approximately 99.7% of the observations will fall within three standard deviations of the mean.
In this case, we know that the mean trash generated per day is 3.8 pounds with a standard deviation of 1.5 pounds.
To find the range within which 95% of the observations fall, we can multiply the standard deviation by two, and then add/subtract it from the mean. Mathematically, it can be shown as:
Range = Mean ± (2 * Standard Deviation)
Substituting the values, we get:
Range = 3.8 ± (2 * 1.5)
Calculating further:
Range = 3.8 ± 3
So, the range within which 95% of the observations will fall is approximately from (3.8 - 3) to (3.8 + 3), which is equal to 0.8 pounds to 6.8 pounds.
Hence, between 0.8 pounds and 6.8 pounds is where 95% of the observations are expected to fall, assuming a bell-shaped distribution.