Revise Probabilities Based on Sample Information

question 18

Multiple Choice

Revise probabilities based on sample information.
-A mid-size company is transitioning to a new ERP system. Consequently, company
Files need to be modified and / or updated so as to be compatible for transfer to the new
System. The company is considering three alternatives to deal with this extra work load.
The difficulty level associated with file modification and transfer will affect the decision,
And initially the company believes there is a 20% chance the file modifications will be
Easy, a 40% chance that they will be moderately difficult and a 40% that they will be
Extremely difficult. The company decides to hire a consultant to review a sample of old
Files and provide her opinion as to whether the modifications required will be extensive
Or minor. Suppose the probabilities associated with her professional opinion are as
Follows: P (Minor | Easy) = 0.80, P (Minor | Moderately Difficult) = 0.50 and P (Minor |
Extremely Difficult) = 0.20. In other words, the chance that she will say the
Modifications required are minor given that the transfer will indeed be easy, moderately
Difficult and extremely difficult are 0.80, 0.50, and 0.20, respectively. What is the
Probability that the difficulty of the file modifications and transfer will be extremely
Difficult given that the consultant believes the modifications required are minor?

• A) 0.56
• B) 0.20
• C) 0.08
• D) 0.44
• E) 0.18

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Definitions:

Preliminary Sample

An initial sample drawn from a population, often used to test procedures or make preliminary estimates before a larger study.

Interval Estimate

An estimate of a population parameter that provides a range of values within which the parameter is expected to lie, often associated with a specific confidence level.

Estimated σ

Approximation of the standard deviation (σ), a measure of the dispersion or variation of a distribution.

Normal Probability Distribution

A bell-shaped probability distribution, also known as Gaussian distribution, that is fully defined by its mean and standard deviation.