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Stats: Consider a certain river. Let H be the height of the river’s water line...?
Consider a certain river. Let H be the height of the river’s water line. Whenever H > 12 a flood occurs. Historically, it is found that H is normally distributed with mean 0 and standard deviation sigma. It’s also found that 2.5% of days have flooding. Suppose sigma goes up by 10%. How much will the percentage of flooding days increase?
1 Answer
- GuyLv 78 years agoFavorite Answer
The top 2.5% of the standard normal curve corresponds to a z-score of 1.96 (from the z-table).
z = (x - mean)/SD
1.96 = (12 - 0)/SD
SD = 12/1.96 = 6.12244898
When this increases by 10%, the new standard deviation is 6.7347.
The probability that H > 12 is the same as the probability that z > (12 - 0)/6.7347 = 1.78, which can be found using a z-table.
I will use my TI-83:
normalcdf(1.78,999) = .0375
The increase in the percentage of flooding is then .0375 - .025 = .0125 = 1.25%
Answer: 1.25%