Question

1. In each of the following cases, determine whether the variable of interest has a binomial distribution. If it does, give the values of the parameters n and p. If it doesn't, explain why not.
(a) You are dealt a five-card poker hand. X = the number of Diamonds in your hand.
(b) You randomly select one card from each of ten different decks of playing cards. X = number of Clubs selected.

Answer 1

(c) Heights of females in some population follow a normal distribution with a mean of 65 inches and standard deviation of 1.5 inches. We take a random sample of three women.

X = number of women in the sample shorter than 64 inches.

(d) A boy asks the same girl to go out on a date every day for a week.

X = the number of times the girl agrees to go on the date.

(e) A multiple choice exam has 30 questions with choices (A, B, C, D and E). An unprepared student guess all of the answers.

X = the number of answers he gets correct.

Answer 2

Do you have the notes to describe the conditions under which binomial distribution applies? There are several criteria, all of which must be satisfied.
We cannot go by guess work. @AprilZ

Answer 3

@AprilZ You still need help?

Answer 4

Yes. @mathmate Binominal Setting: 1.The experiment consits of a sequence of n trails, where n is fixed in advance of the experiment.
2) There are only two possible outcomes for each
trial (a success or a failure).
3) The trials are independent, so that the outcome of
any particular trial does not influence the outcome
of any other trial.
4) The probability p of a success is constant from
trial to trial.
An experiment for which these four conditions are
satisfied is called a binomial experiment.

Answer 5

Excellent!
Now you can examine each case, give your verdict, and I can help you if necessary.

Answer 6

@mathmate
(a)no it is not binomial distribution. Because n is not defined.

(b) n = 10
p = 0.25

(c) n = 3
p = probability of shorter than 64 inches.

(d) It is not binomial distribution. It is not independent.

(e) n = 30
p = 0.2

This is all my answers, but I'm not sure whether they are correct. Could you help me to take a look at them please.
Thank you!!

Answer 7

(a) n = 5 is given. Can you reconsider?
(b) is correct

Answer 8

(c) n=3, and p has to be determined from theNormal distribution table for \Z=-2/3

Answer 9

(d) exactly, \(normally\) each trial is not independent due to emotions.

Answer 10

(e) is perfect!

Cool, you seem to have a good handle of things!

Answer 11

so what is p for (a)?

Answer 12

p is variable, depending on how many diamonds have been given out at each point.

Answer 13

ok! Thanks for your help!!

Answer 14

You're welcome, April! :)