A contractor is interested in the total cost of a project on which he intends to bid. He estimates that materials will cost Kshs. 250,000/= and that his labor will be Kshs. 9,000/= per day. If the project takes X days to complete, the total labor cost will be 9,000X shillings and the total cost of the project in shillings will be: C = 250,000 + 9000X. The contractor forms subjective probabilities of likely completion times for the project as shown below. Completion Time (X) days1011121314Probability0.10.30.30.20.1 RequiredFind the mean and variance for the completion time X. Find the mean, variance and standard deviation for total cost.

Given: If the project takes X days to complete, the total labor cost will be 9,000X shillings The…

Answered: A contractor is interested in the total…

College Algebra

10th Edition

ISBN:9781337282291

Author:Ron Larson

Publisher:Ron Larson

Chapter8: Sequences, Series,and Probability

Section: Chapter Questions

Problem 41CT: On a game show, a contestant is given the digits 3, 4, and 5 to arrange in the proper order to form...

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A contractor is interested in the total cost of a project on which he intends to bid. He estimates that materials will cost Kshs. 250,000/= and that his labor will be Kshs. 9,000/= per day. If the project takes X days to complete, the total labor cost will be 9,000X shillings and the total cost of the project in shillings will be: C = 250,000 + 9000X. The contractor forms subjective probabilities of likely completion times for the project as shown below.

Completion Time (X) days	10	11	12	13	14
Probability	0.1	0.3	0.3	0.2	0.1

Required

Find the mean and variance for the completion time X.
Find the mean, variance and standard deviation for total cost.

Definition Definition Measure of central tendency that is the average of a given data set. The mean value is evaluated as the quotient of the sum of all observations by the sample size. The mean, in contrast to a median, is affected by extreme values. Very large or very small values can distract the mean from the center of the data. Arithmetic mean: The most common type of mean is the arithmetic mean. It is evaluated using the formula: μ = 1 N ∑ i = 1 N x i Other types of means are the geometric mean, logarithmic mean, and harmonic mean. Geometric mean: The nth root of the product of n observations from a data set is defined as the geometric mean of the set: G = x 1 x 2 ... x n n Logarithmic mean: The difference of the natural logarithms of the two numbers, divided by the difference between the numbers is the logarithmic mean of the two numbers. The logarithmic mean is used particularly in heat transfer and mass transfer. ln x 2 − ln x 1 x 2 − x 1 Harmonic mean: The inverse of the arithmetic mean of the inverses of all the numbers in a data set is the harmonic mean of the data. 1 1 x 1 + 1 x 2 + ...

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