a.
To construct: a box and whisker plot for each data set.
a.

Answer to Problem 42E
The box and whisker plot for original design
The box and whisker plot for new design
Explanation of Solution
Given:
Original Design
15.1, 78.3, 56.3, 68.9, 30.6, 27.2, 12.5, 42.7, 72.7, 20.2, 53.0, 13.5, 11.0, 18.4, 85.2, 10.8, 38.3, 85.1, 10.0, 12.6
New Design
55.8, 71.5, 25.6, 19.0, 23.1, 37.2, 60.0, 35.33, 18.9, 80.5, 46.7, 31.1, 67.9, 23.5, 99.5, 54.0, 23.2, 45.5, 24.8, 87.8
Concept Used:
The formulas to compute the lower
Where, n is the number of observations.
Median will be 3
Lower quartile will be the median of lower half.
Upper quartile will be the median of upper half.
Calculation:
Ordered data of Original Design
10.0, 10.8, 11.0, 12.5, 12.6, 13.5, 15.1, 18.4, 20.2, 27.2, 30.6, 38.3, 42.7, 53.0, 56.3, 68.9, 72.7, 78.3, 85.1, 85.2
Here n is 20, minimum value is 10.0 and maximum value is 85.2.
Median will be
Lower quartile will be
Upper quartile will be
Median will be
The box plot for the provided data set can be constructed as:
Ordered data of new Design
18.9, 19.0, 23.1 23.2, 23.5, 24.8, 25.6, 31.1, 35.3, 37.2, 45.5, 46.7, 54.0, 55.8, 60.0, 67.9, 71.5, 80.5, 87.8, 99.5
Here n is 20, minimum value is 18.9 and maximum value is 99.5.
Median will be
Lower quartile will be
Upper quartile will be
The box plot for the provided data set can be constructed as:
b.
To Explain: the difference between the given box and whisker plots constructed.
b.

Answer to Problem 42E
Explanation of Solution
Given:
Original Design
15.1, 78.3, 56.3, 68.9, 30.6, 27.2, 12.5, 42.7, 72.7, 20.2, 53.0, 13.5, 11.0, 18.4, 85.2, 10.8, 38.3, 85.1, 10.0, 12.6
New Design
55.8, 71.5, 25.6, 19.0, 23.1, 37.2, 60.0, 35.33, 18.9, 80.5, 46.7, 31.1, 67.9, 23.5, 99.5, 54.0, 23.2, 45.5, 24.8, 87.8
The box and whisker plot for original design
The box and whisker plot for new design
Interpretation:
The above constructed box plot shows that the box and whisker plot of original design is more spread out with the median 28.9 then the box and whisker plot of new design.
It can also be concluded that the life of original design is lower than the lifetime of new design.
Chapter 13 Solutions
EBK PRECALCULUS W/LIMITS
- 2. Consider the following: Prove that x, x2, and 1/x are the solutions to the homogeneous equation corresponding to x³y"" + x²y" + 2xy' + 2y = 2x4. b. use variation of parameters to find a particular solution and complete the general solution to the differential equation. I am interested in process. You may use a computer for integration, finding determinants and doing Kramer's.arrow_forward3. A spring is stretched 6 in. by a mass that weighs 8 lb. The mass is attached to a dashpot mechanism that has a damping constant of 0.25 lb-sec./ft. and is acted on by an external force of 4 cos 2t lb. a. Set-up the differential equation and initial value problem for the system. b. Write the function in phase-amplitude form. C. Determine the transient solution to the system. Show your work. d. Determine the steady state of this system. Show your work. e. Is the system underdamped, overdamped or critically damped? Explain what this means for the system.arrow_forward4. Suppose that you have a circuit with a resistance of 20, inductance of 14 H and a capacitance of 11 F. An EMF with equation of E(t) = 6 cos 4t supplies a continuous charge 60 to the circuit. Suppose that the q(0)= 8 V and the q'(0)=7. Use this information to answer the following questions a. Find the function that models the charge of this circuit. b. Is the circuit underdamped, overdamped or critically damped?arrow_forward
- 1. Solve the initial value problem: y" -11y' + 30y = x³e6x y(0) 11, y'(0) = 36 =arrow_forwardWhat is the particular solution to the differential equation y′′ + y = 1/cos t ?arrow_forwardWhich of the following is the general solution to y′′ + 4y = e^2t + 12 sin(2t) ?A. y(t) = c1 cos(2t) + c2 sin(2t) + 1/8 e^2t − 3t cos(2t)B. y(t) = c1e^2t + c2e^−2t + 1/4 te^2t − 3t cos(2t)C. y(t) = c1 + c2e^−4t + 1/12 te^2t − 3t cos(2t)D. y(t) = c1 cos(2t) + c2 sin(2t) + 1/8 e^2t + 3 sin(2t)E. None of the above. Please include all steps! Thank you!arrow_forward
- Show that i cote +1 = cosec 20 tan 20+1 = sec² O २ cos² + sin 20 = 1 using pythagon's theoremarrow_forwardFind the general solution to the differential equationarrow_forwardcharity savings Budget for May travel food Peter earned $700 during May. The graph shows how the money was used. What fraction was clothes? O Search Submit clothes leisurearrow_forward
- Exercise 11.3 A slope field is given for the equation y' = 4y+4. (a) Sketch the particular solution that corresponds to y(0) = −2 (b) Find the constant solution (c) For what initial conditions y(0) is the solution increasing? (d) For what initial conditions y(0) is the solution decreasing? (e) Verify these results using only the differential equation y' = 4y+4.arrow_forwardAphids are discovered in a pear orchard. The Department of Agriculture has determined that the population of aphids t hours after the orchard has been sprayed is approximated by N(t)=1800−3tln(0.17t)+t where 0<t≤1000. Step 1 of 2: Find N(63). Round to the nearest whole number.arrow_forward3. [-/3 Points] DETAILS MY NOTES SCALCET8 7.4.032. ASK YOUR TEACHER PRACTICE ANOTHER Evaluate the integral. X + 4x + 13 Need Help? Read It SUBMIT ANSWER dxarrow_forward
- Calculus: Early TranscendentalsCalculusISBN:9781285741550Author:James StewartPublisher:Cengage LearningThomas' Calculus (14th Edition)CalculusISBN:9780134438986Author:Joel R. Hass, Christopher E. Heil, Maurice D. WeirPublisher:PEARSONCalculus: Early Transcendentals (3rd Edition)CalculusISBN:9780134763644Author:William L. Briggs, Lyle Cochran, Bernard Gillett, Eric SchulzPublisher:PEARSON
- Calculus: Early TranscendentalsCalculusISBN:9781319050740Author:Jon Rogawski, Colin Adams, Robert FranzosaPublisher:W. H. FreemanCalculus: Early Transcendental FunctionsCalculusISBN:9781337552516Author:Ron Larson, Bruce H. EdwardsPublisher:Cengage Learning





