Question

At a new exhibit in the Museum of Science, people are asked to choose between 73 or 175 random draws from a machine. The machine is known to have 98 green balls and 61 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 70% of the draws result in a green ball. [You may find it useful to reference the z table.]

a. Calculate the probability of getting more than 70% 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 73 or 175 draws for the game? 73 balls 175 balls

Answer 1

Total number of balls: 98+61 = 159

The probability of getting green ball in a single draw is

P(green) = 98/ 159 = 0.6164

(a)

For 73 draws, that is for n=73:

The sampling distribution of sample proportion will be approximately normal with mean

and standard deviation

The z-score for is

The probability of getting more than 70% green balls is

For 175 draws, that is for n=175:

The sampling distribution of sample proportion will be approximately normal with mean

and standard deviation

The z-score for is

The probability of getting more than 70% green balls is

(b)

With 73 draws we have greater chance to get 70% or more balls so you should choose 73 draws for the game.