Binomial probability Distribution

[Guest]

Consider each of the following distributions. If the distribution is binomial show how it has all the characteristics necessary. If the distribution is not binomial explain why not.

i) The probability distribution for the number of hearts drawn when 5 cards are selected without replacement from a pack of 52 playing cards.


ii) The probability distribution for the number of people believing in astrology when a random sample of 40 is taken and it is known that 22% of people do believe in astrology.

iii) The probability distribution for the number of year 12 students who will enter university if 20 year 12 students are chosen randomly. University entrance record show that 30% of year 12 students continue on to University.

iv) The probability distribution for the outcomes of the treatment for back pain. One hundred patients are treated. The probability of a cure is 0.4, while the probability of an improvement but not a complete cure is, 0.3.

 

[pka]

Properties of binomial distribution:
1 The experiment must have a fixed number of identical trials.
2 Each trial must result in one of two outcomes: success or failure.
3 The probability of success on any trial is constant.
4 The trials are independent events.
5 The values of the distribution are the number of successes.

Now you take time to examine each of the four problems.
You tell us which one satisifies each of these five.
If any fail one or more of the five, explain why.