5. For a six-sided die it is assumed that each of the sides has an equal chance of landing uppermost when the die is rolled.
- Write down the probability function for the random variable \(X\), the number showing on the uppermost side after the die has been rolled.
- State the name of the distribution.
A student wishing to check the above assumption rolled the die 300 times and for the sides 1 to 6 , obtained the frequencies \(41,49,52,58,37\) and 63 respectively.
- Analyse these data and comment on whether or not the assumption is valid for this die. Use a \(5 \%\) level of significance and state your hypotheses clearly.
(8)