A laboratory scale is known to have a standard deviation of

A laboratory scale is known to have a standard deviation of = 0.004 gram in repeated weighings. Scale readings in repeated weighings are Normally distributed, with mean equal to the true weight of the specimen. Six weighings of a specimen on the scale give an average of 3.414 grams. A 95% confidence interval for the true weight is which of the following?
3.414 ± 0.00269

3.414 ± 0.00131    

3.414 ± 0.04704

3.414 ± 0.00320

3.414 ± 0.00022

3.414 ± 0.01920

3.414 ± 0.00784

Solution

CI = x ± Z a/2 * (sd/ Sqrt(n))
Where,
x = Mean
sd = Standard Deviation
a = 1 - (Confidence Level/100)
Za/2 = Z-table value
CI = Confidence Interval
Mean(x)=3.414
Standard deviation( sd )=0.004
Sample Size(n)=6
Confidence Interval = [ 3.414 ± Z a/2 ( 0.004/ Sqrt ( 6) ) ]
= [ 3.414 - 1.96 * (0.0016) , 3.414 + 1.96 * (0.0016) ]
= [ 3.414 ± 0.003120 ]
= [ 3.4108,3.4172 ]

ANS: 3.414 ± 0.00320