Question

# The probability that someone will win a certain game is p = 0.37 p=0.37 . Let...

The probability that someone will win a certain game is p = 0.37 p=0.37 . Let x x be the random variable that represents the number of wins in 655 655 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 655 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 655 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 655 655 times. (Round your answers to 1 place after the decimal point, if necessary.) usual minimum value = usual maximum value =

Solution :

Given that,

p = 0.37

q = 1 - p = 1 - 0.37 = 0.63

n = 655

Using binomial distribution,

Mean = = n * p = 655 * 0.37 = 242.4

Standard deviation = = n * p * q = 655 * 0.37 * 0.63 = 12.36

Using range rule thumb,

minimum value = μ - 2σ

minimum value = 242.4 - 2 * 12.36

minimum value = 217.7

maximum value =  μ + 2σ

maximum value = 242.4 + 2 * 12.36

maximum value = 267.1

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