Question

At a new exhibit in the Museum of Science, people are asked to choose between 75 or 166 random draws from a machine. The machine is known to have 88 green balls and 82 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.

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

b. Would you choose 75 or 166 draws for the game?

• 75 balls

• 166 balls

Answer 1

Answer:

Given,

p = ( 88) / (88 + 82)

p = 0.52

a )To calculate the probability of getting more than 60% green balls

For n = 75

P(X > 0.6) = P(Z > (0.6 - 0.52)/sqrt(0.52 * (1 - 0.52) / 75))

= P(Z > 1.39)

= 0.0822644

P(X > 0.6) = 0.0823

Now,  n = 200

P(X > 0.6) = P(Z > (0.6 - 0.52)/sqrt(0.52*(1-0.52)/200))

= P(Z > 2.265)

= 0.0117563

P(X > 0.6) = 0.0118

b )

Here I would choose 75 balls ,

Since the probability is high.

so n = 75