# Confidence Interval for Mean of Infinite Population n = 100, X̄ = 57.25, s = 2.5 & 95% confidence

The *probability *of unknown population parameter expected to lie between the confidence interval 56.76 and 57.74. 56.76 and 57.74 are the lower and upper limits of the confidence interval for *mean* of infinite population estimated from *sample size* n = 100, sample mean X̄ = 57.25 sample *standard deviation* s = 2.5 & *Z-score* of confidence level for 95% = 1.960

## Work with Steps for n = 100, X̄ = 57.25, s = 2.5 & 95% confidence

The complete work with step by step calculation for sample size n = 100, sample mean X̄ = 57.25 sample standard deviation s = 2.5 & Z-score of confidence level for 95% = 1.960 to estimate the confidence interval for mean of infinite population in statistical experiments.__Workout :__

step 1 Address the formula input parameters and values

Sample size n = 100

Sample mean X̄ = 57.25

Sample standard deviation σ = 2.5

Z-score for 95% confidence level = 1.960

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

= 57.25 ± 1.9602.5√100

step 3 Simplify the above expression

= 57.25 ± 1.9602.510

= 57.25 ± 1.960 x 0.25

= 57.25 ± 0.49

57.25 + 0.49 = 57.74 or 57.25 - 0.49 = 56.76

The lower limit is 56.76 and

The upper limit is 57.74

56.76 & 57.74 are the lower and upper limits of the confidence interval for n = 100, X̄ = 57.25, s = 2.5 & Z = 1.960