The COVID-19 outbreak has been impacting our lives in many ways. In Australia, 75% of people believe that the first social lockdown measures worked well to control the spread of the disease across the country. A random sample of 25 people was selected and asked their opinion on the following statement 'the social lockdown measures worked well to control the spread of the disease'.

a. If the random variable X is the number of people in the sample who believe that the lockdown worked well to control the spread of the disease, say why X could be considered to have a binomial distribution.

b. State the value/s of parameter/s of X.

c. Calculate (using the appropriate statistical tables) the probability that twenty people in the sample agreed with the statement.

d. Calculate (using the appropriate statistical tables) the probability that more than half the people surveyed disagreed with the statement.

e. Say what the value you obtained in part d actually means, in terms of the result (or outcome) of such a survey.