# Confidence Interval for Mean of Finite Population for n = 120, X̄ = 65.25, s = 1.5, N = 1000 & 99% confidence

*probability*of unknown parameter of population expected to lie between the confidence interval 64.9191 and 65.5809. The values 64.9191 and 65.5809 are the lower and upper limits of the confidence interval for

*mean*of finite population estimated from

*sample size*n = 120, mean X̄ = 65.25,

*standard deviation*s = 1.5 population size N = 1000 &

*Z-score*of confidence level for 99% = 2.575 to estimate the confidence interval for mean of finite population.

## Work with Steps for n = 120, X̄ = 65.25, s = 1.5, N = 1000 & 99% confidence

The complete work with step by step calculation for sample size n = 120, sample mean X̄ = 65.25, standard deviation s = 1.5, population size N = 1000 & Z-score for confidence level 99% = 2.575 to estimate the confidence interval for mean of finite population in statistical experiments.__Workout :__

step 1 Address the formula input parameters and values

Sample size n = 120

Sample mean X̄ = 65.25

Sample standard deviation σ = 1.5

Population sample size N = 1000

Z-score for 99% confidence level = 2.575

Population size N = 1000

step 2 Substitute sample size, point estimate of population mean, sample standard deviation & Z-score in the below confidence interval formula

= 65.25 ± 2.5751.5√120√(1000 - 120)/(1000 - 1)

step 3 Simplify the above expression

= 65.25 ± 2.5751.5√120√880/999

= 65.25 ± 2.5751.510.9545√0.8809

= 65.25 ± 2.575 x 0.1369 x 0.9386

= 65.25 ± 0.3309

65.25 + 0.3309 = 65.5809 or 65.25 - 0.3309 = 64.9191

The lower limit is 64.9191 and

The upper limit is 65.5809

64.9191 & 65.5809 are the lower and upper limits of the confidence interval for n = 120, X̄ = 65.25, s = 1.5, N = 1000 & Z = 2.575