A cat rescue centre keeps a record of how many kittens are born in each litter over a year.  The bar chart summarises the figures.

Consider the mean, mode and median of the number of kittens per litter. 

Determine which one of the statements is true.

One of the two solutions to the equation is   .

Determine the second solution.

A)

B)

C)

D)

A coin is tossed 7 times.

Calculate the number of possible combinations that gives 4 heads and 3 tails.

For random variable X, use the following statistics to calculate its coefficient of skewness based on central moments.

E(X) = 3.940

E(X2) = 21.466

skew(X) = E[(X - μ)3] = 6.008

Using simple iteration, based on trial and improvement, the cubic equation below can be solved:

2x3 + 5x2 +7x - 12 = 0 

Solve for x to 6 decimal places.

X is a random variable with expected value E(X).

Identify which of the following is not a valid method for calculating the variance of X.

A discrete random variable can only take the values 2,3,4 or 5. The probabilities associated with some of the outcomes are: P(X=2) = 0.2, P(X=3) = 0.3, P(X=5) = 0.1.

For a randomly drawn value of X, calculate P(X > 3).

Calculate the sum of the following non-terminating progression:

2/10, 2/40, 2/160, 2/640,...

Assuming the position of the first quartile of an appropriately ordered dataset is given by 

and the position of the third quartile of an appropriately ordered dataset is given by

Calculate the range and interquartile range of the above dataset.