Question

The probability that someone will win a certain game is p = 0.67 p=0.67 . Let x x be the random variable that represents the number of wins in 1286 1286 attempts at this game. Assume that the outcomes of all games are independent. What is the mean number of wins when someone plays the game 1286 times? (Round your answer to 1 place after the decimal point, if necessary.) μ μ = What is the standard deviation for the number of wins when someone plays the game 1286 times? (Round your answer to 2 places after the decimal point, if necessary.) σ σ = Use the range rule of thumb (the " μ ± 2 σ μ±2σ " rule) to find the usual minimum and maximum values for x x . That is, find the usual minimum and maximum number of wins when this game is played 1286 1286 times. (Round your answers to 1 place after the decimal point, if necessary.)

usual minimum value =

usual maximum value =

Answer 1

probability that someone will win a certain game is p = 0.67

x : number of wins in 1286  attempts at this game

n : Number attempts

x follows Binomial distribution with n=1286 and p =0.67 (q=1-p=1-0.67=0.33)

Mean of Binomial distribution = np

Standard deviation =

mean number of wins when someone plays the game 1286 times : = np = 1286x0.67 = 861.6

standard deviation for the number of wins when someone plays the game 1286 times : =

usual minimum value = = 861.2-2x16.86 = 827.9

usual maximum value = = 861.2+2x16.86 = 895.3