Respuesta :
Answer: 38416
Step-by-step explanation:
The formula to find the sample size in a normally distributed population :-
[tex]n=(\dfrac{z^*\times \sigma}{E})^2[/tex] , where [tex]\sigma[/tex] = 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
[tex]n=(\dfrac{1.96\times0.01}{0.0001 })^2\\\\=38416[/tex]
Hence, the minimum sample size should be 38416 .
The minimum sample size is 38416 and this can be determined by using the formula of the sample size in a normally distributed population.
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 weighings is computed.
- Suppose the scale readings are Normally distributed, with unknown mean m and standard deviation σ = 0.01 grams.
The formula of the sample size is given by:
[tex]\rm n=\left({\dfrac{z\times \sigma}{E}} \right)^2[/tex]
where [tex]\sigma[/tex] is the standard deviation, z is the critical z-value, and E is the margin of error.
Now, substitute the values known terms in the above formula.
[tex]\rm n=\left({\dfrac{1.96\times 0.01}{0.0001}} \right)^2[/tex]
Simplifying the above expression in order to determine the value of 'n'.
n = 38416
So, the minimum sample size is 38416.
For more information, refer to the link given below:
https://brainly.com/question/21344417
