Question

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 ¯ x x¯ of the weighings is computed. Suppose the scale readings are Normally distributed, with unknown mean m m and standard deviation σ = 0.01 σ=0.01 grams. How large should n n be so that a 95% confidence interval for m m has a margin of error of ± 0.0001 ±0.0001 ?

Answer 1

Answer: 38416

Step-by-step explanation:

The formula to find the sample size in a normally distributed population :-

$n=(\dfrac{z^*\times \sigma}{E})^2$ , where  $\sigma$ = Population standard deviation from the prior study.

z* = critical z-value , E = Margin of error.

As per given , we have

The scale readings are Normally distributed, with unknown mean m m and standard deviation σ = 0.01 grams.

E =  ±0.0001

Critical z- value for  95% confidence interval : z* = 1.96

Substitute all values in formula , we get

$n=(\dfrac{1.96\times0.01}{0.0001 })^2\\\\=38416$

Hence, the minimum sample size should be 38416 .