The probability of winning the Powerball jackpot on a singlegiven play is 1/175,223,510. Suppose the powerball jackpot becomeslarge, and many people play during one particular week. In fact,180 million tickets are sold that week. Assuming all the ticketsare independent of one another, then the number of tickets shouldbe binomially distributed. The values of the parameters n and p inthis binomial distribution are:
n=
p=
Then, use the binomial distribution to find the probability thatthere is one or more winning tickets sold.
______
If X = the number of winning tickets sold, find the mean andstandard deviation of the random variable X.
Mean of X =Â Â
Standard deviation of X =Â Â
On the other hand, since the \"times\" between winning tickets shouldbe independent of one another, the number of winning tickets perweek could reasonably be modeled by a Poisson distribution.
The value of the parameter lambda in this Poisson distributionwould be _____
The standard deviation of the number of tickets sold in a week(using the Poisson model) is _________
What does the Poisson model predict is the probability of havingone or more winning tickets sold? _____
Then, use the binomial distribution to find the probability thatthere is one or more winning tickets sold. _________
