At a new exhibit in the Museum of Science, people are asked to choose between 73

Question

At a new exhibit in the Museum of Science, people are asked to choose between 73 or 200 random draws from a machine. The machine is known to have 88 green balls and 78 red balls. After each draw, the color of the ball is noted and the ball is put back for the next draw. You win a prize if more than 60% of the draws result in a green ball.

Calculate the probability of getting more than 60% green balls.(Round intermediate calculations to 4 decimal places, “z” value to 2 decimal places, and final answer to 4 decimal places.)

b.

a.

Calculate the probability of getting more than 60% green balls.(Round intermediate calculations to 4 decimal places, “z” value to 2 decimal places, and final answer to 4 decimal places.)

n Probability 73 200

b.

Would you choose 73 or 200 draws for the game? 73 balls 200 balls

Explanation / Answer

p = ( 88) / (88 + 78) = 0.53

a ) n = 73

P(X > 0.6) = P(Z > (0.6 - 0.53)/sqrt(0.53*(1-0.53)/73)) = P(Z > 1.20) =1- 0.8849=0.1151

  n = 200

P(X > 0.6) = P(Z > (0.6 - 0.53)/sqrt(0.53*(1-0.53)/200)) = P(Z > 1.98) =1- 0.9761=0.0239

b ) I would chose 73 balls , since probability is high.

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