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Question about proportion involving Math (Statistics)?
An Adults in North America is approximately normally distributed, with a mean of 12 gallons and a deviation of 4 gallons.
- What proportion of adults use more than 16 per week?
- What proportion of adults uses less than 4 gallons per week?
2 Answers
- ?Lv 71 year ago
16 gallons is exactly 1 standard deviation above the mean of 12.
So the question amounts to what percentage in a normal distribution are more than 1 SD. Now look at this
https://studiousguy.com/wp-content/uploads/2019/04...
Adding approximate tail percentages on the right, result is ~ 15.86%
A slightly more accurate result from this normal distribution right tail table
http://www2.stat.duke.edu/~rcs46/lectures_2015/14-...
is (1 + 0.1587)* 100 = 15.87%
- stanschimLv 71 year ago
1. z = (16 - 12) / 4 = 1
P(z > 1) = 0.1586 or about 16 out of 100 adults.
2. z = (4 - 12) / 4 = -2
P(z < -2) = 0.0228 or about 2 out of 100 adults.
