The factor of safety, F,, of a rock slope is commonly thought of as the ratio of the maximum load or stress that a slope can sustain to the actual maximum load or stress that is applied during a design lifetime. Suppose that an extensive statistical study has determined that the actual F, for rock slopes in the Cape Breton Highlands against sliding has a Weibull distribution with median 2.947 and 3 = 0.3. a) What is A for this distribution? b) What is the probability that the F, is less than 1 for a randomly selected rock slope? c) Suppose that design standards are such that slopes having factors of safety in excess of 2.0 are considered to be "safe". What fraction of rock slopes in the Cape Breton Highlands would then be considered "unsafe" and so thus in need of remediation?

The average annual rainfall in New York City follows a normal distribution with a mean of 49.9 inches and a standard deviation of 9.5 inches. On what percentage of years can we expect there to be between 40.4 and 59.4 inches of rain in New York City? (A) 100% B) 99.7% C) 95% D) 68%

Answer for question D) and E)

A boat capsized and sank in a lake. Based on an assumption of a mean weight of 133 Ib, the boat was rated to carry 70 passengers (so the load limit was 9,310 Ib). After the boat sank, the assumed mean weight for similar boats was changed from 133 lb to 174 lb. Complete parts a and b below. a. Assume that a similar boat is loaded with 70 passengers, and assume that the weights of people are normally distributed with mean of 181.1 Ib and a standard deviation of 38.6 lb. Find the probability that the boat is overloaded because the 70 passengers have mean weight greater than 133 lb The probability isO: (Round to four decimal places as needed.) b. The boat was later rated to carry only 17 passengers, and the load limit was changed to 2,958 Ib. Find the probability that the boat is overloaded because the mean weight of the passengers is greater than 174 (so that their total weight is greater than the maximum capacity of 2,958 Ib). The probability is. (Round to four decimal places as needed.)…