Question

Let 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

The first step is to convert the distribution to one that applies to distances over a period of 7 years. The 7 year distribution has
\[\large \mu=11\times7=77\ feet:\ \ \ \ \sigma=2\times7=14\ feet\]
The z-score for a distance of 90 feet is found from:
\[\large z=\frac{X-\mu}{\sigma}=\frac{90-77}{14}=0.9286\]
Now you need to refer to a standard normal distribution table to find the required probability.