Question 1. Identify each of the following scenarios as: A) Binomial experiments

Question

Question 1.

Identify each of the following scenarios as: A) Binomial experiments or can be reduced to binomial experiments (Identify n and p)

B) Not binomial experiments BUT can we approximated using binomial experiments,(Explain why and Identify n and p)

C) Not binomial and cannot be approximated using binomial distribution (Explain why)

a.An urn contains 50 marbles (25 green, 15 white, and 10 red), we select without replacement 2 marbles. We are interested in green marbles.

b.Tossing a coin 100 times to see how many heads occur

c.Drawing 5 cards with replacement from a deck and getting a heart

d. Drawing 5 cards without replacement from a deck and getting a heart

e.Drawing 2 cards without replacement from a deck and getting a heart

f.Asking 100 people if they smokeg. Asking 100 people which brand of cigarettes they smoke

h.Testing four different brands of aspirin to see which brands are effective

i.Testing one brand of aspirin by using 10 people to determine whether it is effective

Explanation / Answer

a) Not binomial experiments BUT can we approximated using binomial experiments because we selected only 2 marbles and the value of p doesn't change much (i.e. from 0.5 to 0.49) so we can approximate the experiment as binomial experiment. n = 2, p = 0.5

b) Binomial experiments or can be reduced to binomial experiments, The experiment consists of n repeated trials. Each trial can result in just two possible outcomes. n = 100, p = 0.5

c) Binomial experiments or can be reduced to binomial experiments, The experiment consists of n repeated trials. Each trial can result in just two possible outcomes. n = 5, p = 0.25

d) Not binomial and cannot be approximated using binomial distribution since we have 5 trials and with each trial the probability of success decreases and the difference between initial and final probability of success is significant (i.e. from 0.25 to 0.214)

Related Questions

Navigate

• Browse (All)
• Browse Q
• Subjects

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.