Refer to the Journal of Waterway, Port, Coastal, and Ocean Engineering (March/April, 2013) study of coastal sea level rise, Exercise 5.6. Recall that the acceleration Y in sea level rise (standardized between 0 and 1) was modeled using the following density function:

ƒ(y) = 6y(1 – y), 0 < y < 1

a. Find Interpret the result.    

b. Find the variance of Y.

c. Use the Empirical Rule to estimate P(μ – 2σ < Y < μ + 2σ).

d. Find the actual probability, P(μ – 2σ < Y < μ + 2σ). How does the answer compare to the result in part c?

Data From Exercise 5.6:

Coastal sea level rise. 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