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Probability Problem

  • 17-01-2012 6:55pm
    #1
    SantryRed
    Closed Accounts Posts: 13,224 ✭✭✭✭


    Hi lads. Have a quick question in regards a test I have tomorrow. Just doing some study and am stumped for the last part of this Q. Thanks,


    (b)
    If 80% of TV viewers are known to watch the technology program
    Tomorrow Today and 5 TV viewers are picked at random, what are the
    probabilities that
    (i) All of them watch Tomorrow Today
    (ii) At least 3 of them watch Tomorrow Today
    (iii) Exactly 2 of them watch Tomorrow Today
    (iv) At most 3 of them watch Tomorrow Today
    [81

    (c)
    If 500 TV viewers are picked at random, calculate the approximate
    probability that between 380 and 420 of them watch Tomorrow Today.


Comments

  • #2
    Yakuza
    Registered Users, Registered Users 2 Posts: 5,141 ✭✭✭Yakuza


    Without giving the answers, here are the approaches you can take to the questions you ask:

    I'm assuming you're doing a stats course of some sort, so hopefully most of the below won't read like double Dutch.

    EDIT - I've just noticed your post is two days old and the test was yesterday; I hope it went well...;)

    (b) - Treat this as a binomial experiment with probabilty of success 0.8.

    i) What is the probability of 5 sucesses in 5 trials?
    ii) At least 3 successes means 3 or 4 or 5. You can do this in two ways - work out the probabilities of 3 and 4 sucesses and add them to that of 5 which you've already worked out *or* work out the probs for 0, 1 and 2 successes and take them from 1
    iii) What is the probability of 2 sucesses in 5 trials? (you may already have calc'd this before)
    iv) I'll leave this one to you.

    (c) For large sample size N (in this case 500), in most cases the binomial distribution approximates very closely to the normal distribution.
    For a Binomial Dist with size N and p(success) of p, then this can be approximated with a normal distribution (Np, Np(1-p)), or Norm(400, 80) - i.e. normally distributed with mean 400 and standard deviation sqrt(80) (roughly 8.944).

    So, what is the area under the bell curve between (380-400)/8.944 and (420-400)/8.944? Hint:
    It's quite close to 1


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