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blondinia [14]
2 years ago
10

The temperature of a solution will be estimated by taking n independent readings and averaging them. Each reading is unbiased, w

ith 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? Round the answer to the next largest whole number.
Physics
1 answer:
Viktor [21]2 years ago
3 0

Answer:

68 readings.

Explanation:

We need to take this problem as a statistic problem where the normal distribution table help us.

We can start considerating that X is the temperature of the solution, then

0.9 = P(|\bar{x}-\mu|

0.9 = P(\frac{|\bar{x}-\mu|}{\frac{\sigma}{\sqrt{n}}}

0.9 = P(|Z|

For a confidence level of 90% our Z_{critic} is 1.645

Therefore,

\frac{0.1}{\frac{\sigma}{\sqrt{n}}} = 1.645

Substituting for \sigma = 5 and re-arrange for n, we have that n is equal to

n=(\frac{1.645\sigma}{0.1})^2

n=\frac{(1.645)^2(0.5)^2}{0.1^2}

n=67.65

n=68

We need to make 68 readings for have a probability of 90% and our average is within 0.1\°\frac

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