Calculators & Converters

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

    Confidence Interval Calculator

    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
    Z-score for confidence level

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

    formula to estimate confidence interval or limits or range

    = 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

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