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 σ =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?

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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/