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Probability and Statistics : Scatter Plot, Line of Best Fit, Extrapolation and Forecasting

11. An automaker guarantees its particular type of automotive transmissions for 90,000 km. Tests have shown that such transmissions have an average life of 135,000 km with a standard deviation of 22,500 km. If the lives of these transmissions are normally distributed, what is the probability that a car will be returned to the company for transmission work while it is still under warranty?

12. The B.A. Company sells an imported desk calculator on a franchise basis and performs preventive maintenance and repair service on this calculator. The data below have been collected from 17 recent calls on users to perform routine preventive maintenance service. For each call, information was collected on the number of machines serviced and the total time (in minutes) spent by the service person:

Observation 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17
# Machines 7 6 5 1 5 4 7 4 2 8 5 2 5 7 1 4 5
# Minutes 97 86 78 10 75 62 101 53 33 118 65 25 71 105 17 49 68

a. Create a scatter plot of these data to investigate the relationship between how many machines an office has and how long it takes to perform preventative maintenance. Put # Machines on the x-axis and # Minutes on the y-axis.
b. Use a straightedge to sketch the line that seems to best approximate the data points. Then estimate the slope and the y-intercept of that line, and write the equation of the line you sketched.
Use the line from b. to predict the time needed to perform routine preventive maintenance for an office with 3 machines

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Solution Summary

Scatter Plots, Lines of Best Fit, Extrapolation and Forecasting are investigated. The solution is detailed and well presented.

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