MATHS COURSEWORK

Maths Coursework



Maths Coursework

Solution 1(a)

The mean temperature will be higher because the data is skewed rightwards.

IQR = 98.6° - 97.85° = 0.75°. Since 1.5(IQR) = 1.125°, the fences are 97.85° - 1.125° = 96.725° and 98.6° + 1.125° = 99.725°. The lowest temperature (96.7°) being added to the data set is smaller than the lower fence (96.725°) so it is an outlier on the low end. The highest temperature (99.2°) being added to the data set is not above the upper fence (99.725°) so it is not an outlier on the high end.

Solution 1(b)

Passenger. The age is less than one year.

Passengers. The age is 21 years.

Cyclist. The age is [Range=40].

Pedestrian. IQR= Q3-Q1 i.e. 65-20=45.

Passengers. There are outliers present in the passengers that have increased the range of the data and also the passengers group contains people up to almost 100 years.

Solution 2

To move the particles around a simple method is Euler iteration, where you store the positions and velocities. Position = position + velocity*dt; where dt is the change in time since the last frame. It is best to keep dt fixed, and interpolate between points for the renderer if you can... this will reduce stability issues and make collision detection easier. To reflect a particle off of a wall, check if its x components or y components of position will exceed the bounds and then flip the sign of the other component of the velocity, e.g.

if(Math.Abs(position.x_component + velocity.x_component * dt) > x_bound) velocity.y_component = -velocity.y_component;

if(Math.Abs(position.y_component + velocity.y_component * dt) > y_bound)

velocity.x_component = -velocity.x_component;

For colliding the particles with each other a distance check is probably best, triggering reflection once the distance is too small. i.e. If they get too close they collide. Reflect the velocity components as though the particles were spheres, so the normal for reflection is the difference of their positions.

Solution 2(b)

If the probability of the bad outcome is too large (for example, more than 5%), men will need to consider hiring additional staff or take other steps necessary to reduce the customer waiting time.

The data is best described by the Exponential distribution with parameter ?=0.04. The cumulative distribution function of this distribution can be used to calculate the probability of both outcomes. The Exponential CDF is:

F(x) = 1 - exp(-? * x)

The probability of the first outcome can be calculated as:

P(X=60) = F(60) = 1 - exp(-0.04 * 60) = 0.91 = 91%,

and the probability of the second outcome is as follows:

P(X>60) = 1 - F(60) = 0.09 = 9%,

meaning that 9% of customers wait on hold for more than 60 seconds. The analysis results suggest that the probability of the bad outcome is too high, and men make the decision to hire extra support staff.

Solution 3

The size of the carrot has been placed on the horizontal axis because the size is an independent variable. The independent variables are placed on the horizontal axis and the response variables are placed on the vertical axis. There is a positive association between the size of the ...