Rising sea levels are a threat to coastal cities in the United States. Consequently, for planning purposes it is important to have accurate forecasts of the future rise in sea level. The Journal of Waterway, Port, Coastal, and Ocean Engineering (March/April, 2013) published a study which used a statistical probability distribution to model the projected rise in sea level. The acceleration Y in sea level rise (standardized between 0 and 1) was modeled using the following density function:

f(y) = cy(1 – y), 0 < y < 1

a. Find the value of c for this probability distribution.

b. Find the cumulative distribution function,

c. Compute and interpret this value.