A voltage measurement consists of the sum of a constant unkn

A voltage measurement consists of the sum of a constant unknown voltage and a Gaussian-distributed noise voltage of zero mean and variance 16 muV^2. Twenty five independent measurements are made and a sample mean of 100 mu V is obtained. Find the corresponding 95% confidence interval.

Solution

Confidence Interval
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)=100
Population Standard deviation( sd )=4
Sample Size(n)=25
Confidence Interval = [ 100 ± Z a/2 ( 4/ Sqrt ( 25) ) ]
= [ 100 - 1.96 * (0.8) , 100 + 1.96 * (0.8) ]
= [ 98.432,101.568 ]