SOLUTION: You really struggle remembering to bring your lunch to work. Each day seems to be independent as to whether you remember to bring your lunch or not. The chance that you forget your

Question 1199363: You really struggle remembering to bring your lunch to work. Each day seems to be independent as to whether you remember to bring your lunch or not. The chance that you forget your lunch each day is 39.9%.
Consider the next 45 days. Let X be the number of days that you forget your lunch out of the 45 days. Calculate the following:
I managed to find μX but I have no idead on how to find the other answers.
μX : 17.955
σX :
P(X=18) :
P(X<21) :
P(X>15) :
P(15≤X≤20) :

Answer by ikleyn(53751)   (Show Source): You can put this solution on YOUR website!
.

This problem is on Binomial distribution.

If you don't know how to approach this problem with its several questions, it means that
you are unfamiliar with Binomial distribution.

At this site, there are several lessons where many similar problems were solved and presented in all details

    - Simple and simplest probability problems on Binomial distribution
    - Typical binomial distribution probability problems
    - Solving problems on Binomial distribution with Technology (using online solver)

Look into these lessons.

After reading/learning from these lessons, you will be able to solve such problems on your own, which is your
PRIMARY MAJOR GOAL visiting this forum (I believe).

If you will have questions after reading these lessons, do not hesitate to post your questions to the forum.

///////////////////

Regarding μX, use the formula  μX = n*p,   


    where n is the number of trials  (45 in your problem), 
    and p is "the probability of individual success at each single trial",
    p = 0.399 in your problem.



Regarding  σX,  use the formula  σX = .

See the links

https://stats.libretexts.org/Bookshelves/Introductory_Statistics/Book%3A_Statistics_Using_Technology_(Kozak)/05%3A_Discrete_Probability_Distributions/5.03%3A_Mean_and_Standard_Deviation_of_Binomial_Distribution

https://study.com/skill/learn/how-to-calculate-the-standard-deviation-of-a-binomial-distribution-explanation.html

https://study.com/skill/learn/how-to-calculate-the-standard-deviation-of-a-binomial-distribution-explanation.html

It is written in each and every textbook on Statistics and in thousands Internet web-sites.

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