Modelling Suitability etc

With reference to the histogram, state, giving a reason. whether or not tomas’s model could be suitable [His model is a normal distribution and the histogram is skewed to the left quite a bit]

(Not suitable as) data is not symmetric or is skew (normal is symmetric) B1 2.4

(“Even” distribution or a diagram on its own is not enough so B0)

State a condition needed for T to be modelled by [a binomial model] [T is the number of packets of sweets that contain sweets in each box]

Comment in context about either independence or random packing e.g.

“prizes must be placed in packets at random/independently of each other”

or about constant probability e.g.

“the probability of a packet containing a prize is constant/ the same/fixed

Comment on the suitability [of model]

comparision of model’s prediction to actual value suggests good or not good

State assumptions that BLAH needs to make to use her binomial model

Binomial conditions hidden in CONTEXT

Use the value calculated from the data and the value predicted by the model to comment on the suitability of the model

compare values and if not roughly same say ‘so model may not be suitable’

[the probability that the time, T, is less than 2 given its greater than zero greater than the probability that T is less than 2] hence explain why this normal distribution may not be a good model for T

The current model suggests non-negligible/significant probability of T values < 0 which is impossible

Explain why distribution B(14, 0.27) might not be a reasonable model for the number of days without rain for a 14 day summer event. (this p was calculated as the proportion of days without rain for cmaborne from the large data set in one year)

A correct reason referring to

• independence (needs context as to what is independent) eg consecutive 14 days

unlikely to be independent.

• probability [of rain] not being constant.

• Allow a comment that conveys the idea that the proportion of days with no rain

will be different over the year.

With reference to the scatter diagram [quadratic ish] state, giving a reason, whether or not the regression line of [linear form] is an appropriate model for these data

No – since POINTS seem to follow a curve/quadratic (rather than a line)

or since points are “non-linear” but regression line/ model is linear

or e.g. between (t = 5 and 7 )height drops by much more than 2.56 m

or e.g. gradient is positive up to t = 3.5 (line gradient < 0)

or e.g. gradient is positive initially (line gradient < 0)

or e.g. gradient is positive and then negative

explain why a binomial distribution might not be a good model for the number of days in a 10day period when it is raining at 6 am

Rainfall on consecutive days may not be independent