(a) If you toss a fair coin four times would you expect the proportion of heads

Question

(a) If you toss a fair coin four times would you expect the proportion of heads (or tails) always to be exactly 0.5 (yes or no)? (b, c, d, e) What other proportions would you probably find on carrying out this experiment a few more times? If you repeated this experiment again but, instead of tossing the coin only four times, you tossed it a very large number of times (a million, say). (f) What proportion of heads (or tails) would you expect to find this long series approaching increasingly closely? (g) What is the name of the 'law' that deals with proportions emerging from this last kind of experiment? (h) What kind of distribution is obtained by sampling from this ("binomial") distribution, assuming the sample meets the necessary criteria? (i, j) What are the 'necessary criteria' to be used for a sample from a binomial distribution to be distributed approximately Normally?

Explanation / Answer

a)

No

b)

0

c)

0.25

d)

0.75

e)

1

f)

0.5

g)

binomial distribution

h)

normal distribution

i)

if the sample is large

and/or

j)

the proportion of success is close to 0.5

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