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To assess the accuracy of a laboratory scale, a standard weight that is known to weigh 1 gram is repeatedly weighed a total of n times and the mean of the weighings is computed. Suppose the scale readings are normally distributed with unknown mean and standard deviation g. How large should n be so that a 95% confidence interval for has a margin of error of ± 0. 0008?.



Answer :

The formula for the sample size in a normally distributed population can be used to calculate the minimal sample size, which is 38416.

Given,

  • To assess the accuracy of a laboratory scale, a standard weight known to weigh 1 gram is repeatedly weighed a total of n n times and the mean of the weighs are computed.
  • Suppose the scale readings are Normally distributed, with unknown mean m and standard deviation σ = 0.01 grams.

Sample size formula;

n = ((z × σ) / E)²

When z is the crucial z-value, E is the margin of error, and σ is the standard deviation.

Now change the known values in the formula above.

n = ((1.96 × 0.01) / 0.0001)²

n = 38416

Therefore,

The minimum sample size for the distribution is 38416.

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