In an accelerated life test, units are operated under extreme conditions unit failure. In one such test, 12motors were operated under high temperature conditions. The ambient temperature (in ?) and lifetimes (in hours) are presented in the following table. Temperature Lifetime 40 851 45 635 50 764 55 708 60 469 65 661 70 586 75 371 80 337 85 245 90 129 95 158 a. Construct a scatterplot of lifetime (?) versus temperature (?). Verify that a linear model is appropriate. b. Compute the least-squares line for predicting lifetime from temperature. c. Compute the fitted values and the residual for each point. d. If the temperature is increased by 50? by how much would you predict the lifetime to increase or decrease? e. Predict the lifetime for a temperature of 730?. f. Should the least-squares line be used to predict the lifetime for a temperature of 1200?? If so, predict the lifetime. If not, explain why not. g. For what temperature would you pre
Continuous Probability Distributions
Probability distributions are of two types, which are continuous probability distributions and discrete probability distributions. A continuous probability distribution contains an infinite number of values. For example, if time is infinite: you could count from 0 to a trillion seconds, billion seconds, so on indefinitely. A discrete probability distribution consists of only a countable set of possible values.
Normal Distribution
Suppose we had to design a bathroom weighing scale, how would we decide what should be the range of the weighing machine? Would we take the highest recorded human weight in history and use that as the upper limit for our weighing scale? This may not be a great idea as the sensitivity of the scale would get reduced if the range is too large. At the same time, if we keep the upper limit too low, it may not be usable for a large percentage of the population!
6. In an accelerated life test, units are operated under extreme conditions unit failure. In one such test, 12motors were operated under high temperature conditions. The ambient temperature (in ?) and lifetimes (in hours) are presented in the following table.
Temperature Lifetime
40 851
45 635
50 764
55 708
60 469
65 661
70 586
75 371
80 337
85 245
90 129
95 158
a. Construct a scatterplot of lifetime (?) versus temperature (?). Verify that a linear model is appropriate.
b. Compute the least-squares line for predicting lifetime from temperature.
c. Compute the fitted values and the residual for each point.
d. If the temperature is increased by 50? by how much would you predict the lifetime to increase or decrease?
e. Predict the lifetime for a temperature of 730?.
f. Should the least-squares line be used to predict the lifetime for a temperature of 1200?? If so, predict the lifetime. If not, explain why not.
g. For what temperature would you predict a lifetime of 500 hours.
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