Question

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 _________ 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
binomial random variable with mean E(X) = and Let X be the number of card selections with outcome "General." Then X is a standard deviation o =________

Answer 1

1, this is a binomial experiment.

Explanation:

this is a binomial experiment. Since it is general outcome, the probability of success is 0.50, that is 50 percent.

we have that X follows the binomial distribution

X ~ Binomial(n = 3, p = 0.50)

we have 3 outcomes( general, applied, theoretical).

mean = E(X)

= np

= 3(0.5)

= 1.5

standard deviation = σ = √np(1-p)

= √3(0.5)(1-0.5)

= √1.5(0.50)

= √0.75

= 0.8660

the mean = 1.5

the standard deviation = 0.8660