Helen believes that the random variable C, representing cloud cover from the large data set, can be modelled by a discrete uniform distribution - Edexcel - A-Level Maths Statistics - Question 1 - 2018 - Paper 2
Question 1
Helen believes that the random variable C, representing cloud cover from the large data set, can be modelled by a discrete uniform distribution.
(a) Write down the ... show full transcript
Worked Solution & Example Answer:Helen believes that the random variable C, representing cloud cover from the large data set, can be modelled by a discrete uniform distribution - Edexcel - A-Level Maths Statistics - Question 1 - 2018 - Paper 2
Step 1
Write down the probability distribution for C.
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Answer
The probability distribution for a discrete uniform distribution with values from 0 to 8 (representing different levels of cloud cover) is given by:
P(C=c)=91forc=0,1,2,3,4,5,6,7,8
This is because there are 9 possible values.
Step 2
Using this model, find the probability that cloud cover is less than 50%.
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Answer
To find the probability that cloud cover is less than 50%, we consider values of C from 0 to 4 (since 4 is the highest value representing less than 50%). Thus, the probability is:
Comment on the suitability of Helen’s model in the light of this information.
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Given that the actual proportion of days with cloud cover of less than 50% was found to be 0.315, while the model predicts 0.555, it indicates that Helen’s model may not accurately represent the real-world data. The model overestimates the likelihood of lower cloud cover, suggesting that it is not suitable for this data set.
Step 4
Suggest an appropriate refinement to Helen’s model.
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A suitable refinement to Helen's model could involve using a non-uniform distribution that accounts for variations in cloud cover based on location or time of year. This could involve more complex modeling techniques that incorporate historical weather patterns or other relevant data to improve accuracy.
