Statistics Assignment

Questions: 1. A basketball player has the following points for seven games: 20, 25, 32, 18, 19, 22, and 30. Compute the following measures: a) Compute the sample mean (the average of the points of each game) b) Compute the sample median c) Compute the variance and the standard deviation 2. Suppose during weekends, 55 percent of adults go to the beach, 45 percent go to the cinema, and 10 percent go to both the beach and the cinema. a) What is the probability that a randomly chosen adult does not go to the cinema? b) What is the probability that a randomly chosen adult go to the beach or the cinema or both? c) What is the probability that a randomly chosen adult doesn't go to the beach or the cinema? 3. A Financial Consultant has classified his clients according to their gender and the composition of their investment portfolio (primarily bonds, primarily stocks, or a balanced mix of bonds and stocks). The proportions of clients falling into the various categories are shown in the following table: Portfolio Composition Gender Bonds Stocks Balanced Male 0.18 0.20 0.25 Female 0.12 0.10 0.15 One client is selected at random, and two events A and B are defined as follows: A: The client selected is male. B: The client selected has a balanced portfolio. Find the following probabilities: Find the following probabilities: a) P(A) b) P(B) c) P(A or B) d) P(A or B) e) P(A/B) Answers: (1). a) Let X be the variable, then mean of X is sum(X)/n, n being the no. of observations. Thus mean =23.71429 b) Median is that value of X say which such that proportion of observations above y is 0.5. After arranging the data in increasing order, we get Median =22. c) The variance of X is , m is the sample mean. Thus variance =30.2381 Standard deviation = =5.498918 (2). a) Let A be the event of going to beach and B be the event of going to cinema. We are required to find P(B) =1-P(B) =0.55 b) Here we are to find P(AUB) =P(A) +P(B) P(AB) =0.55+0.45-0.1 =0.9 c) We are to find P(AB) =1-P(AUB) =1-0.9 =0.1 (3). A: The client selected is male. B: The client selected has a balanced portfolio. Find the following probabilities: a) P(A) =18+0.20+ 0.25=0.63 b) P(B) =0.15+0.25 =0.4 c) P(AUB) =P(A) +P(B) P(AB) =0.63+0.4-0.25 =0.78 d) P(AUB) =P(A) +P(B) P(AB) =0.63+0.4-0.25 =0.78 e) P(A/B) =(AB)/P(B) =0.25/0.4 =0.625.