The depth of water, H, behind a gravity dam is normally distributed with a mean of 100' and variance of 2,500 ft2. The total hydrostatic pressure against the dam is F=?H2/2, where ? is the unit weight of water (62.4 pcf).
a. Calculate the mean value of F and an expression for its standard deviation.
b. If the height of water exceeds 110', there will be a dam overflow. Calculate the probability associated with this event.
c.If the designer wants to be at least 75% sure that the overflow does not occur,what should the designer choose for the height of the dam?