Like Many Professionals, the Clergy in Mainline Protestant Churches Have

question 11

Essay

Like many professionals, the clergy in mainline Protestant churches have pension
plans. Due to the nature of the ministry, investment strategies may involve what are
known as "screens." Screens are rules that prevent a pension fund administrator from
investing in corporations that are involved with, for example, alcohol, gambling,
tobacco and weapons of mass destruction. Ministers may elect to invest in two broad
categories: "regular" and "social purpose" funds, which would typically use screens
in their investment strategy. The use of screens may reduce their monthly benefit at
retirement.
The data below are from a survey of ministers about their support in principle for the
use of such screens. Each minister asked if the screens should be applied to the
regular funds, the social purpose funds, both, or neither. The ministers were also
classified by the current percentage of their investments in the social purpose funds:
0%, 10 - 59%, 60% or greater. $$\begin{array} { | l | c | c | c | c | } \hline \text { Use screens for: } & \begin{array} { l } 0 \% \\\text { group }\end{array} & \begin{array} { l } 10 - 59 \% \\\text { group }\end{array} & \begin{array} { l } 60 + \% \\\text { group }\end{array} & \text { Total } \\\hline \begin{array} { l } \text { Social purpose } \\\text { funds only }\end{array} & 70 & 94 & 58 & \mathbf { 2 2 2 } \\\hline \begin{array} { l } \text { Both social } \\\text { purpose } \\\text { and regular funds }\end{array} & 83 & 235 & 266 & \mathbf { 5 8 4 } \\\hline \text { Neither } & 47 & 11 & 3 & \mathbf { 6 1 } \\\hline \text { Uncertain } & 23 & 15 & 6 & \mathbf { 4 4 } \\\hline \text { Total } & \mathbf { 2 2 3 } & \mathbf { 3 5 5 } & \mathbf { 3 3 3 } & \mathbf { 9 1 1 } \\\hline\end{array}$$ a) What is the probability that a minister selected at random from those who
participated in the survey was uncertain about the use of screens?
b) What is the probability that a minister selected at random from those who
participated in the survey was in the 60+% group and supported the use of screens
for social purpose funds only?
c) What is the probability that a minister selected at random from those who
participated in the survey felt the screens should be used for social purpose funds
only or for both social purpose and regular funds, given that they were in the 10-
59% group?
d) What is the probability that a randomly selected "uncertain" minister would be in
the 0% group?

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Definitions:

Actual Direct Labor Cost

The total expense of labor directly involved in the manufacturing of a product, excluding indirect costs such as supervisory personnel.

Variable Overhead Rate Variance

The difference between the actual variable overhead incurred and the expected (or standard) variable overhead based on the actual level of activity.

Variable Overhead

Costs that fluctuate with production output levels, such as utilities or indirect materials, but are not directly tied to specific units produced.

Variable Overhead Rate Variance

The difference between the actual variable overhead costs and the standard variable overhead costs allocated based on a predetermined rate.