A lottery game asks gamblers to pick a number between 40 and 180. If a gambler p

Question

A lottery game asks gamblers to pick a number between 40 and 180. If a gambler picks the right number, the gambler wins $500. Each of the possible numbers has an equal chance of being the winning number. a. What is the probability that the winning number will be 53? (Round your answer to 4 decimal places.) b. What is the probability that the winning number will be between 81 and 150, inclusively? (Round your answer to 4 decimal places.) c. What is the mean value of the winning number? (Round your answer to 1 decimal place.) d. What is the variance of the winning number? (Round your answer to 3 decimal places.)

Explanation / Answer

Since the number needs to be picked between 40 and 180,

each number has the possibility of 1/139 or 0.0072 of being the winning number

the winning number being between 81 and 156 inclusively is 76/139 or 0.5468

Since each number is equally likely it just the average or 110.

Variance is E[X^2] - E[X]^2 = 1610.

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