Question

Individual Age Gender (Male=1) Family Size Cigarettes/Day Alcohol/Day Total Claims 1 25 1 2 0 3 1 2 28 0 7 0 1 0 3 20 0 3 10 0 9 4 53 1 1 0 0 5 5 48 0 3 5 2 12 6 54 1 3 0 0 2 7 56 1 4 0 0 0 8 35 1 3 10 1 10 9 50 0 6 0 0 6 10 39 1 6 0 0 1 11 56 1 7 0 3 4 12 29 0 5 0 2 4 13 60 1 1 0 1 3 14 29 1 5 0 1 1 15 21 1 2 20 1 17 16 23 1 4 0 1 1 17 38 1 4 0 1 8 18 62 1 4 0 0 7 19 24 0 1 0 3 7 20 53 0 7 0 1 6

ai) Find the mean number of claims made by the sample of smokers and nonsmokers in the group separately.(i.e mean of smokers, mean of nonsmokers)

ii) What is the standard deviation of family size for this population of workers? (standard deviation of popuation) Standardize by converting your “X” values into “Z” values to see whether their historical values match up well with the new company. Use a Z table Hint: use the (ai) and (aii) values along with the means and standard deviations you calculated.

b) First find the Z-value for smokers.

c) And now the Z for nonsmokers.

d) Using your Z-table, find the probability that a nonsmoker will make fewer than 6 claims.

e) Next, find the probability that a smoker will make more than 11 claims.

f) Final Recommendation: This firm will be more risky than the current customer risk pool. True or False

Answer 1

I am assuming that you are using excel for this question. If you want help with any other software or manual calculations, let me know in the comment section.

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My data is stored in sheet range of A1:G21 as shown -

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a) i)

Now, you can use 'AVERAGEIFS' function to get the conditional average using following function.

=AVERAGEIFS(G2:G21,E2:E21,"=0")

This would give you the mean of 'Total Claims' if 'Cigarettes/Day' = 0. Which is the mean for non-smokers.

And, thus use the function =AVERAGEIFS(G2:G21,E2:E21,">0") for the non smokers.

You get the mean value of 3.5 and 12 for non-smokers and smokers respectively.

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ii)

We need population standard deviation for the variable 'Family Size'. So we use the following formula -

=STDEV.P(D2:D21)

And this would give you the value = 1.946792.

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The standardized value of 'X' would be -

Where is value calculated in a(i) while is the standard deviation calculated in (ii).

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b)

For smokers -

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c)

For non-smokers, the Z value is -

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d)

For non smokers, mean = 3.5

From Z-table you get this value to be 0.8997.

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e)

For smokers, mean = 12.

And so, we get -

P(X > 11) = 1 - 0.3050 = 0.695.

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f)

True.

As the probabiility of making more claims is significant, so it will be more risky than the current customer risk pool.