Question

Problem # 5 (12 points) A random sample of 130 musicians was selected. Each musician was categorized by gender and according to how they learned to play their instruments. Each musician was asked to select only one gender category (male or female) and only one, most relevant, learning mode (self-taught, studied in school or private instruction).The data is presented in the table below. Total Self-taught Private Instruction Studied in School 72 22 38 12 Female 58 15 24 19 Male 130 37 62 31 Total a. What proportion of musicians have NOT been self-taught? (2 points) b. What proportion of musicians are female and received private instruction in learning how to play their instruments? (2 points) What proportion of male musicians learned to play their instrument in school? c. (2 points) d. Are the events "musician is female" and "learned how to play their instrument in school" mutually exclusive? Justify your answer. (2 points) e. The sample data suggests that the probability of having learned to play an instrument by being self-taught depends on musician's gender: male musicians are more likely to have been self-taught than female musicians. Find relevant percentages to back up this claim. (4 points)

Answer 1

Proportion of musicias that have not beaen set taught 4/130 - 1- 31 T30 076154 female and recievad private 6 Ropasthion of musicians who aue intution in laaming ha to play their instruments 22/130 O.1692 3 11 11 CPropestion of maleImusicans tho launed to play their instrument in schoel 24/58 0.4 38 11 d Mutually exclusive vents a ocur Aimultaneously Sine disgoint everts f e at the hama time they Cannot Play female musiian Could have leainad hous to their instrument in school. So, thay a metualy exclurive events ane not e % of musicans (male) who learned how to instrument an by sulf tarziht 19/30=0.146/5 (famale usho leantd hou to play 0.0923 0146 instrument % of mousicians an y a-taught- 12/20n male musicians Hence, twe Can claim that to hawe been tought are more than female musicians