Chapter 5, Problem 4ICA

1. a. If estimating the amount of time to design a new product, should you err on the high side or the low side?
2. b. If estimating the switching speed of the transistors for a faster computer, is it better to err on the low side (slower switching) or high side?
3. c. How many square yards of fabric are needed to cover the seats in a typical minivan? Is it better to err on the high side or the low side?
4. d. Estimate the dimensions of the classroom, in feet. Using these values and ignoring the fact that you would not paint over the windows and doors, estimate the gallons of paint required to paint the classroom. A gallon of paint covers 400 square feet. Would it be better to round the final answer up or down to the nearest gallon?

To determine

Find out whether the error should be produced on the high side or the low side while estimating the time required for designing a new product.

Explanation of Solution

Discussion:

While estimating the time required for designing a new product, the error produced should be estimated on the higher side. This is done in order to avoid the holding up of the production of the product.

Conclusion:

Hence, the error should be done on the higher side.

To determine

Find out whether the error should be produced on the high side or the low side while estimating the switching speed of the transistor for a faster computer.

Explanation of Solution

Discussion:

While estimating the switching speed of the transistors of a faster computer, the error produced should be estimated on the lower side. This is done in order to avoid the discrepancy which will arise if we promise a faster speed and are unable to deliver that. Therefore keeping the error on the lower side will be a safer option.

Conclusion:

Hence, the error should be on the lower side while estimating the switching speed of the transistors of a faster computer.

To determine

Determine the number of square yards of fabric required to cover the seats of a typical minivan and also the side in which the error should be.

Explanation of Solution

Discussion:

Consider the common area of fabric for covering a seat is 1.75 square yards and the number of seats in the minivan is 8.Therefore the area of cloth required will be $\begin{array}{l}8\times 1.7\text{5}\text{square}\text{yards}\\ \text{=14}\text{square}\text{yards}\end{array}$

The estimation of the error that can be produced in estimating the size should be done on the higher side to ensure that there is enough material and there is no shortage. This is because in case of shortage it is not necessary that we will get the exact material again.

Conclusion:

Hence, number of square yards of fabric needed is 14 square yards and the error should be made on the higher side.

To determine

Estimate the dimensions of a class in feet and find out if it will be better to round up the final answer up or down the nearest gallon.

Explanation of Solution

Discussion:

Assume the classroom’s size to be 900 square feet. According to the given question a gallon of paint covers over 400 square feet, therefore for estimating the gallon of paint required for painting the classroom, it will be wise to round the final answer up to the nearest gallon. By taking more amount of paint we will be sure to have enough paint for painting the classroom without having to take the effort to get more paint also there are chances that we may not get the exact color if we run out of paints.

Conclusion:

Hence, the dimension of the classroom is 900 square feet and it will be better to round the final answer up to the nearest gallon.