UNIVERSITY OF BOTSWANA FACULTY OF SCIENCE DEPARTMENT OF MATHEMATICS MAT271 INTRODUCTION TO MATHEMATICAL STATISTICS TUTORIAL EXECISES 1 PART I. COUNTING PRINCIPLES I (1) A president and a treasurer are to be chosen from a student club consisting of 50 people. How many different choices of officers are possible if (a) there are no restrictions; (b) A will serve only if he is president; (c) B and C will serve together or not at all; (d) D and E will not serve together? (2) Four married couples have bought 8 scats in the same row for a concert. In how many different ways can they be seated (a) With no restrictions? (b) If each couple is to sit together? (c) If all the men sit together to the right of all the women? (3) You are going on a road trip with 4 friends in a car that fits 5 people. How many different ways can everyone sit if you have to drive the whole way? (4) In how many ways can 4 boys and 5 girls sit in a row if the boys and girls must alternate? (5) In how many ways can 5 different trees be planted in a circle? (6) You are deciding which awards you are going to display in your room. You have 8 awards, but you only have room to display 4 awards. Right now you are not worrying about how to arrange the awards, so the order does not matter. How many ways could you choose the 4 awards to display? (7) How many ways are there to select 3 candidates from 8 equally qualified recent graduates for openings in an accounting firm? (8) How many different ways can the gold, silver, and bronze medals be awarded in an Olympic event with 12 athletes competing? (9) How many different ways could you score a 70% on a 10-question test. where each question is weighted equally and is either right or wrong?

Need parts A, E and F

50 100 150 200 250 300 Distance (in thousands of kilometers) Part A: How many vehicles were rented from Hertz in March? vehicles Part B: How many more vehicles were driven between 50 and 100 thousand kilometers than between 250 and 300 thousand kilometers? vehicles Part C: How many vehicles were driven less than 200 thousand kilometers? vehicles 54% O Type here to search F9 F10 F11 F1 F2 & %23 3 6 7 8 E T. Y S. G M Alt Cto Alt Number of vehicke

Workplace Fatalities in 2013 93% 7% Source: Bureau of Labor and Statistics Women Men Look at the fatalities pie chart below. Which of the following conclusions is correct? 93% of all men who are employed suffer a fatal injury. 7% of all women suffer a fatal injury. 7% of all fatal work injuries are suffered by women.

State Debt and Per Capita Tax An economics student wishes to see if there is a relationship between the amount of state debt per capita and the amount of tax per capita at the state level. Based on the following data, can she or he conclude that per capita state debt and per capita state taxes are related? Both amounts are in dollars and represent five randomly selected states. Per capita debt x       1645    2781    1904    1791    3418 Per capita tax  y       2423    3890    2129    2095    2214     (a) Compute the value of the correlation coefficient. Round your answer to at least three decimal places. r= (b) State the hypotheses. H0 :    H1:    (c) Test the significance of the correlation coefficient at α=0.05 , using The Critical Values for the PPMC Table.  Critical values: ± ▼(Choose one) the null hypothesis.       (d) Give a brief explanation of the type of relationship. There ▼(Choose…