Question

Question 26 University of Oshawa Tech has conducted a survey of its faculty members and has found the following distribution of the number of dependents covered under their health insurance and their monthly cost. Number of People Covered Insurance Plan Probability Monthly Cost 0.45 $130 2 0.25 0.15 $200 $270 3 4 or more ? $350 a) (1pt.) What is the probability that a faculty member has four or more people under insurance? b) (1pt.) What is the average cost of insurance for Oshawa Tech faculty members? c) (2pts.) What is the standard deviation of the cost among Oshawa Tech faculty members?

Answer 1

a) P(Four or more) = 1 - (0.45 + 0.25 + 0.15) = 0.15

b) Average cost = E(X) = 0.45*130 + 0.25*200 + 0.15*270 + 0.15*350 = $ 201.50

c) E(X^{​​​​​​2}) = (0.45)*130² + 0.25*200² + 0.15*270² + 0.15*350² = 46915

Hence,

Variance = E(X^{​​​​​​2}) - [E(X)]² = 46915 - 210.50² = 6312.75

So,

Standard deviation = = $ 79.45

6312.75