Question

et x be a random variable representing movement (in feet per year) of such sand dunes (measured from the crest of the dune). Let us assume that x has a normal distribution with μ = 11 feet per year and σ = 2 feet per year. Under the influence of prevailing wind patterns, what is the probability of each of the following? (Round your answers to four decimal places.) (a) an escape dune will move a total distance of more than 90 feet in 7 years

Answer 1

Given the following which is the mean and standard deviation of the dune’s movement over one year and need to find out what the ten year mean and the standard deviation will be.

The ten-year mean is ten times the one year mean or 110 feet per decade. The ten-year standard deviation is somewhat more complicated. Multiple independent trials accumulate standard deviation as the square root of the number of trials since an unusually high level of movement ten years in a row. The decade is going to be 2 feet per year x square root of ten will result to 6.32 feet.

The answer will to question A. will be:

 

  90           < 110 + z (6.32 feet)

 -20           < z (6.32 feet)

    z            > - 3.16

By using the z table, it shows the probability of 0.9992. This result shows that as 90 feet is lesser than the mean travel that is expected over decade.