Small Business Just Leased A New Color Laser Computer

Question

A Small Business Just Leased A New Computer And Color Laser Printer A small business has leased a new computer and color laser printer for 3 years. The service contract for the computer offers unlimited repairs for a fee of $100 a year plus a $25 service charge for each repair needed. The company’s research indicates that during a given year, 86% of these computers need no repairs, 9% need to be repaired at least once, 4% twice, and 1% three times, and none require more than three repairs. What is the standard deviation in the number of repairs for this kind of computer per year? Round to two decimal places. ---

Dr. Jack HW Helper · Accepted Answer

Introduction Understanding the variability in the number of repairs needed for leased computers is crucial for small business budgeting and service planning. This paper aims to compute the standard deviation of repairs per year for a computer leased under specific service contract conditions, with repair probabilities derived from empirical research. The analysis employs probability concepts, expectation calculations, and variance formulas to arrive at an accurate measure of dispersion in repair needs, facilitating better financial and operational decision-making. Probability Distribution and Data Analysis The given probabilities indicate a discrete probability distribution for the number of repairs, X, per year. Specifically, P(X=0) = 0.86, P(X=1) = 0.09, P(X=2) = 0.04, and P(X=3) = 0.01. These probabilities sum to 1, satisfying the fundamental requirement for a probability distribution. The repair experiences are independent between years, and the probabilities reflect the likelihood of a computer requiring a certain number of repairs within a year. The associated repair costs for each repair are $25 per repair charge plus a fixed $100 annual fee for the service contract. Therefore, for the repair count X, the total repair cost T can be expressed as: $$ T = 100 + 25X $$ with X taking values 0, 1, 2, and 3. Though the costs are relevant for financial analysis, calculating the standard deviation focuses on the variability in the number of repairs, X, which follows a probability distribution identified from the data. Calculations of Expected Value and Variance The mean number of repairs per year, E(X), is calculated as: $$ E(X) = \sum_{i=0}^3 i \times P(X = i) $$ which is: $$ E(X) = 0 \times 0.86 + 1 \times 0.09 + 2 \times 0.04 + 3 \times 0.01 = 0 + 0.09 + 0.08 + 0.03 = 0.20 $$ Next, the second moment E(X^2) is necessary for variance calculation: $$ E(X^2) = \sum_{i=0}^3 i^2 \times P(X = i) $$ \[ E(X^2) = 0^2 \times 0.86 + 1^2 \times 0.09 + 2^2 \times 0.04 + 3^2 \tim

Small Business Just Leased A New Color Laser Computer

A Small Business Just Leased A New Computer And Color Laser Printer

Sample Paper For Above instruction

Introduction

Probability Distribution and Data Analysis

Calculations of Expected Value and Variance

Conclusion

References