5. Four coins are flipped together and the random variable \(H\) represents the number of heads obtained. Assuming that the coins are fair,
- suggest with reasons a suitable distribution for modelling \(H\) and give the value of any parameters needed,
- show that the probability of obtaining more heads than tails is \(\frac { 5 } { 16 }\).
The four coins are flipped 5 times and more heads are obtained than tails 4 times.
- Stating your hypotheses clearly, test at the \(5 \%\) level of significance whether or not there is evidence of the probability of getting more heads than tails being more than \(\frac { 5 } { 16 }\).
Given that the four coins are all biased such that the chance of each one showing a head is 50\% more than the chance of it showing a tail,
- find the probability of obtaining more heads than tails when the four coins are flipped together.