The initial temperature of a certain container is measured
Chapter 5, Problem 4E(choose chapter or problem)
The initial temperature of a certain container is measured to be \(T_{0}\) . The ambient temperature is measured to be \(T_{a}\)
C. An engineer uses Newton's law of cooling to compute the time needed to cool the container to a temperature of
. Taking into account the physical properties of the container, this time (in minutes) is computed to be
\(T=40 \ln \left(\frac{T_{0}-T_{a}}{10-T_{a}}\right)\)
Assume that the temperature measurements \(T_{0}\) and \(T_{a}\) are unbiased and come from normal populations with standard deviation .
a. Generate an appropriate simulated sample of values . Is it reasonable to assume that
is normally distributed?
b. Use the simulated sample to estimate the standard deviation of .
c. If appropriate, use the normal curve to find
confidence interval for the time needed to cool the container to a temperature of
.
Equation transcription:
Text transcription:
T_{0}
T_{a}
T=40 \ln \left(\frac{T_{0}-T_{a}}{10-T_{a}}\right)
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