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Identifying a binomial experiment
In a study conducted by the sponsoring organization of an academic conference, attendees were classified during registration into one of three categories according to their field of interest: General, Applied, or Theoretical. Of the 400 people in attendance, 200 were classified as General, 60 were classified as Applied, and 140 were classified as Theoretical. You randomly select three registration cards (with replacement) of attendees of the conference and record their fields of interest.
This experiment______a binomial experiment.
When you select a registration card, the probabilities associated with each outcome are:
Outcome Probability
General 0.35
Applied 0.45
Theoretical 0.20
Let X be the number of card selections with outcome "General." Then X is a_____binomial random variable with mean E(X) =_____and standard deviation =______.

Sagot :

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Answer:

Step-by-step explanation:

[tex]\text{This experiment is a binomial experiment}}[/tex]

[tex]\text{ The outcome of general = 0.35}[/tex]

[tex]So; If[/tex] [tex]X \sim Binomial (n = 3,p= 0.35)[/tex]

[tex]Then;[/tex]

[tex]Mean,[/tex] [tex]E(X) = np[/tex]

[tex]E(X) = (3)(0.35) \\ \\ E(X) = 1.05[/tex]

[tex]\text{Standard deviation:}[/tex]

[tex]\sigma= \sqrt{np(1-p)} \\ \\ = \sqrt{(3)(0.35)(1-0.35)} \\ \\ =0.826[/tex]

[tex]Thus;[/tex]

[tex]\text{Let X be the number of card selections with outcome "General."}[/tex]

[tex]\mathbf{ Then \ X \ is \ a\ binomial \ random \ variable \ with \ mean \ E(X) \ = \ 1.05}[/tex]

[tex]\mathbf{and \ standard \ deviation = 0.826}[/tex]

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