(Papers) ACET Paper May 2010 "CT3 – Probability & Mathematical Statistics"

Q. 1)

The following amounts are the sizes of claims (in Rs.) on house insurance policies for a certain type of repair.
199, 240, 215, 209, 230, 210, 218, 215, 203, 210, 218, 201, 206, 216, 212

(a) Two statisticians, A and B find the inter quartile range as 10.75 and 12.00 respectively. Comment on whether statistician A or B or both are correct.
(b) Determine the sample mean and sample variance of the data.
(c) Assuming the data to be normally distributed, find the probability of a claim amount exceeding Rs. 230
(d) Empirically find the probability of a claim amount exceeding Rs. 230 and hence comment on your observation when compared with the answer in (c)

Q. 2)

The following is true about the masses of elephants from a sample of 12:

5 elephants weigh 900 kilograms each; 4 elephants weigh 1,000 kilograms each; 3 elephants weigh 1,396 kilograms each.

Show that the empirical skewness coefficient for this sample is 1 [3]

Q. 3)

A test to detect H1N1 virus shows 5% positive result for those not having H1N1 and 100% positive results for those having H1N1. The probability of occurrence of H1N1 is (1/1000).

What is the probability that a person found to have a positive result actually has H1N1 assuming that you know nothing about the person’s symptoms?