Powerball Lottery As of this writing, the Powerball lottery is run in 42 states. If you buy one ticket, the probability of winning is 1/195,249,054. If you buy one ticket each week for 50 years, you play this lottery 2600 times.

a. Find the mean and standard deviation for the number of wins for people who buy a ticket each week for 50 years. Express the results using six decimal places.

b. Would it be unusual for someone to win this lottery at least once if they buy a ticket each week for 50 years?

Answer :

Step 1 :

Given, the Powerball lottery is run in 42 states. If you buy one ticket, the probability of winning is 1/195,249,054. If you buy one ticket each week for 50 years, you play this lottery 2600 times

n = 2600 and p = 1/195,249,054The procedure yields a binomial distribution.

Where, mean = = np = 2600(1/195,249,054)

= 0.000013

Variance = npq

= (2600)(1/195249054)(195249053/195249054

= 0.00001

Standard deviation = =

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