Question

Cookie Crumbles wants to put enough raisins in its raisin cookie dough so that not more than one cookie in a hundred will have no raisins. How many raisins should an average cookie contain, assuming a random distribution of raisins in the dough?

Name: Problem 38, Chapter 3: Probability, Statistics, and Queuing Theory with Computer Science Applications, Second Edition (Computer Science and Scientific Computing)
Uploaded: 2021-11-06T05:05:51-08:00
Duration: 3 min 6 s
Channel: Stanley Enemuo
Description: Cookie Crumbles wants to put enough raisins in its raisin cookie dough so that not more than one cookie in a hundred will have no raisins. How many raisins should an average cookie contain, assuming a random distribution of raisins in the dough?

   Cookie Crumbles wants to put enough raisins in its raisin cookie dough so that not more than one cookie in a hundred will have no raisins. How many raisins should an average cookie contain, assuming a random distribution of raisins in the dough?

Probability, Statistics, and Queuing Theory with Computer Science Applications, Second Edition (Computer Science and Scientific Computing)

Arnold O. Allen 2nd Edition

Chapter 3, Problem 38

Instant Answer

Solved by Expert Stanley Enemuo

11/06/2021

Step 1

We need to ensure that not more than 1 out of every 100 cookies (i.e., not more than 1%) has zero raisins. This can be expressed as the probability \( P(X = 0) \leq 0.01 \), where \( X \) is the number of raisins in a cookie. Show more…

Show all steps

Thanks for your feedback!

Cookie Crumbles wants to put enough raisins in its raisin cookie dough so that not more than one cookie in a hundred will have no raisins. How many raisins should an average cookie contain, assuming a random distribution of raisins in the dough?

Play audio

Feedback

Stanley Enemuo and 74 other educators are ready to help you.

Ask a new question

Labs

Want to see this concept in action?

NEW

Explore this concept interactively to see how it behaves as you change inputs.

View Labs

Key Concepts

Poisson Distribution

The Poisson distribution describes the probability of a given number of events occurring in a fixed interval of time or space, under the assumption that these events occur with a constant mean rate and independently of the time since the last event. It is especially useful for modeling random, infrequent events.

Expected Value in Poisson Distribution

In the context of the Poisson distribution, the parameter ? represents both the mean and the variance, indicating the average number of events (or occurrences) over the interval. This expected value is central to determining the overall likelihood of different outcomes.

Probability of Zero Events

The probability that no events occur, or zero occurrences, in an interval is given by the expression e^(–?). This concept is critical when one wants to control or limit the probability of an event not happening, such as ensuring that almost every sample contains at least one occurrence.

Please give Ace some feedback