QUESTION 4: It is known that 65% of sixth formers think their maths teacher is strict. In a particular sample, 10 pupils are picked at random, and it is required to calculate the probability that less than 3 of the 10 think that their teacher is strict.

a. Name a probability distribution that can be used for modelling this situation, stating one necessary assumption for this model to be valid.

b. Use the model to calculate the required probability using the formula and table of probability distribution for the specific type.

c. Calculate the mean and variance of this distribution.