According to The United States Geological Survey (USGS), the probability that an earthquake: Statistical Methods and Inference Assignment, SUSS, Singapore

Question 1

According to The United States Geological Survey (USGS), the probability that an earthquake measuring magnitude 7.5 on the Richter scale will occur in the Los Angeles area annually is 0.017. Round all results to 4 decimal places.

(a)  In USGS’s prediction, one can apply the binomial distribution B(n, p) to model the number of the earthquakes in n years. Calculate the probability of an earthquake measuring magnitude 7.5 that will hit the Los Angeles area in the next 30 years.

(b)  Calculate the probability that no earthquake measuring 7.5 will occur in the Los Angeles area in the next 10 years.

(c)  Find the probability that one or more earthquakes measuring 7.5 will strike Los Angeles area in the next 30 years.

Question 2

Use the same annual probability of success p = 0.017 of earthquakes of magnitude 7.5 hitting Los Angeles as predicted by USGS in Question 1.

(a)  Using the Poisson Distribution, calculate the probability that at least one earthquake measuring 7.5 will occur in Los Angeles area in the next 30 years.

(b)  Compare the results found in Question 2(a) against the result from Binomial Distribution in Question 1(c). Which answer is “technically” more correct?

Question 3

A researcher wanted to analyse the scores of a particular course at SUSS. The grades follow a normal distribution with mean 𝜇 = 67.97, and standard deviation 𝜎 = 11.5. Round all answers to two decimal places.

(a)  Calculate the percentage of students who scored more than 70 in this exam for this entire cohort.

(b)  If 12% of the cohort were given A’s, compute the lowest possible A grade.

(c)  A random tutorial group of 30 students was selected. The students’ grades are shown in Table Q3. Do you see anything unusual about the grades of this class? Please give your reasons.