1. The owner of a small firm that employs 20 people has decided to begin offerin

Question

1. The owner of a small firm that employs 20 people has decided to begin offering health insurance for her employees. The insurance company that she is choosing to work with has asked her for demographic information of her workers, namely age, gender, family size, history with tobacco, history with alcohol, and the number of healthcare claims made last year by each individual worker. They have tasked you to examine the data and calculate the expectation of the number of claims per year so they can set a group rate for the firm.

a) First find the mean of Age

b) Now find the standard deviation of age. Remember that this is a full population of workers.

c) Find the mean of gender. This will tell us if the firm employs more men or women.

d) Find the standard deviation of gender now. Remember that this is a population.

e) What is the mean family size?

f) What is the standard deviation of family size for this population of workers?

g) What's the average number of cigarettes smoked?

h) Now find the standard deviation of cigarettes smoked by this population of workers.

i) What's the average number of drinks consumed per day?

j) What's the population standard deviation of alcohol consumed?

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

Explanation / Answer

a) 40.15 mean of age

b) 14.213 standard deviation of age

c) male = 13

d) 0.476 standard deviation of gender

e) 3.9 is the mean family size

f) 1.9467 is the standard deviation of family size for this population of workers

g) 2.25 is the average cigrate smoked

h) 5.1173 standard deviation of cigarettes smoked

i) 1.05 2.25 is the average drinks consumed per day

j) 1.0234 is the population standard deviation of alcohol consumed

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