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The temperature of a solution will be estimated by taking
Chapter 4, Problem 9E(choose chapter or problem)
The temperature of a solution will be estimated by taking \(n\) independent readings and averaging them. Each reading is unbiased, with a standard deviation of \(\sigma=0.5^{\circ} \mathrm{C}\). How many readings must be taken so that the probability is 0.90 that the average is within \(\pm 0.1^{\circ} \mathrm{C}\) of the actual temperature?
Equation Transcription:
Text Transcription:
n
sigma = 0.5 degree C
pm 0.1 degree C
Questions & Answers
QUESTION:
The temperature of a solution will be estimated by taking \(n\) independent readings and averaging them. Each reading is unbiased, with a standard deviation of \(\sigma=0.5^{\circ} \mathrm{C}\). How many readings must be taken so that the probability is 0.90 that the average is within \(\pm 0.1^{\circ} \mathrm{C}\) of the actual temperature?
Equation Transcription:
Text Transcription:
n
sigma = 0.5 degree C
pm 0.1 degree C
ANSWER:Solution
Step 1 of 2
Here we have to find the required number of readings must be taken
so that the probability is 0.9 that the average the average is within 0.10c
Given that each reading is unbiased with standard deviation 0.5
Let n is the required number of readings
Let be the average of the n readings
The mean is
The standard deviation is
=0.5/