Correct Answer - Option 2 : 0.354 ± 1.96 × 0.0047
Given
Population size = n = 100
Standard deviation = s = 0.048
Sample size = N = 2000
Confidence interval = 95% for 2000 ball bearings
Average diameter of 2000 balls = 0.354
Formula used
Sx = s/√n(√(N - n)/(N - 1)
Calculation
The population is finite and the sample size is large relative to population size we will have to use the finite population correction factor in calculating.
⇒ The population is unknown, since sample is large (n =100) the distribution of X is approximately normal.
⇒ Sx = 0.048√100[(2000 - 100)/(2000 - 1)
⇒ 0.048/10[(1900/1999) = 0.0047
∴ The 95% CI for the average diameter = 0.354 ± (1.96)(0.0047)