An author receives a contract from a publisher, according to which she is to be paid a fixed sum of $20,000 plus $3.50 for each copy of her book sold. The author judges that her uncertainty about total sales of the book can be represented by a random variable with a mean of 17,000 and a standard deviation of 4,000 books. Find the mean and standard deviation of the total payments she will receive.

Answer:The mean of the total payments she will receive is $79,500.The standard deviation  of the total payments she will receive is $14,000.Step-by-step explanation:Given : An author receives a contract from a publisher, according to which she is to be paid a fixed sum of $20,000 plus $3.50 for each copy of her book sold. The author judges that her uncertainty about total sales of the book can be represented by a random variable with a mean of 17,000 and a standard deviation of 4,000 books.To find : The mean and standard deviation of the total payments she will receive ?Solution : Let 'x' represent total sales of the book.Let 'y' represent the payment to the author.According to question,The mean of the total payments she will receive is given by,[tex]\mu_y=20,000+3.50\mu_x[/tex]Where, [tex]\mu_x=17,000[/tex]Substitute in the equation,[tex]\mu_y=20000+3.50\times 17000[/tex][tex]\mu_y=20000+59500[/tex][tex]\mu_y=79500[/tex]The mean of the total payments she will receive is $79,500.The standard deviation of the total payments she will receive is given by,[tex]\sigma_y=|3.50|\sigma_x[/tex]Where, [tex]\sigma_x=4,000[/tex]Substitute in the equation,[tex]\sigma_y=|3.50|\times 4000[/tex][tex]\sigma_y=14000[/tex]The standard deviation  of the total payments she will receive is $14,000.