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 ? = 0.5°C. How many readings must be taken so that the probability is 0.90 that the average is within ±0.1°C of the actual temperature?
What will be an ideal response?
Let n be the required number of measurements. Let 
be the average of the n measurements.
Then the true value is 
, and the standard deviation is 
Now 
.In any normal population, 90% of the population is within 1.645 standard deviations of the mean.
Therefore 
Since 
.The smallest value of n is therefore n= 68.
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