Asked Jan 25, 2020

Powerball: Poisson Approximation to Binomial There is a 1/292,201,338 probability of winning the Powerball lottery jackpot with a single ticket. Assume that you purchase a ticket in each of the next 5200 different Powerball games that are run over the next 50 years. Find the probability of winning the jackpot with at least one of those tickets. Is there a good chance that you would win the jackpot at least once in 50 years?


Expert Answer

Step 1

The probability of winning the Powerball lottery jackpot with a single ticket is 1/292,201,338. Also, a person purchases a ticket in each of the next 5,200 different power ball games that run over the next 50 years.

Requirements for using the Poisson distribution as an approximation to binomial distribution are as follows:

  • The number of n trials is greater than or equal to 100, that is, n≥100.
  • The mean, np is less than or equal to 10, that is, np≤10.

Where, n is the number of trials and p is the probability of success. If the requirements are satisfied, the Poisson approximation to binomial distribution is used.

Here, the number of trials is 5,200 and is greater than 100. Hence, the first requirement is satisfied.

Statistics homework question answer, step 1, image 1
Step 2

The mean value (µ) is less than 10. Hence, the second requirement is satisfied.

Thus, the Poisson distribution is an approximation to binomial distribution.

Probability of winning with at least one ticket in 50 years:

Define the random variable x as the number of times ...

Statistics homework question answer, step 2, image 1

Want to see the full answer?

See Solution

Check out a sample Q&A here.

Want to see this answer and more?

Solutions are written by subject experts who are available 24/7. Questions are typically answered within 1 hour.*

See Solution
*Response times may vary by subject and question.
Tagged in

Related Statistics Q&A

Find answers to questions asked by student like you
Show more Q&A

Q: A 2x2 ANOVA produced the following F-ratios. FA = 1, FB = 5, FAxB = 8. For all three tests, dfbetwee...

A: The critical value for the F-ratios FA = 1.From the given information the value of test statistics i...


Q: A variable of a population is normally distributed with mean µ and standard deviation σ. a. Identify...

A: Hey there! Thank you for posting the question. Since your question has more than 3 parts, we are sol...


Q: In each of Exercises, assume that the population standard deviation is known and decide whether use ...

A:  The following assumptions are required for the large sample confidence interval about the mean to b...


Q: Preliminary data analyses indicate that you can reasonably use a t-test to conduct each of the hypot...

A: The null and alternative hypotheses are stated below:


Q: The results of a recent survey indicate that the average new car costs $23,000, with a standard devi...

A: It is given that the mean new car cost is $23,000 with a standard deviation of $3,500.


Q: Answer true or false to each statement. Give reasons for your answers. a. Two variables that have th...

A: (a)Here, it is observed that the different types of distributions have the same mean and standard de...


Q: Suppose x1 and x2 are predictor variables for a response variable y. a. The distribution of all poss...

A: Consider,The multiple regression line can be written as:


Q: In each of Exercises, explain the effect on the margin of error and hence the effect on the accuracy...

A: Effect on margin of error:If the level of confidence increases then corresponding critical value wil...


Q: The number of gallons of paint that Home Depot sells in a given day is normally distributed with a m...

A: Click to see the answer