Problem 20BSC

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 = 1/195,249,054

The 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 = =

= 0.003649

b) We have to find the minimum usual value and maximum usual value

i.e , Minimum usual value

= - 2

= 0.000013 - 2(0.003649)

= -0.007285

Maximum usual value

= + 2

= 0.000013 + 2(0.003649)

= 0.007311

It is unusual to buy a ticket each week for 50 years and win at least once.

Because one win is outside the range of usual values.