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23 June, 17:29

A study of a local high school tried to determine the mean number of text messages

that each student sent per day. The study surveyed a random sample of 114 students

in the high school and found a mean of 195 messages sent per day with a standard

deviation of 73 messages. Determine a 95% confidence interval for the mean,

rounding all values to the nearest whole number.

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  1. 23 June, 17:34
    0
    182 ≤ x ≤ 208 Confidence Interval

    Step-by-step explanation:

    Normal Distribution

    Sample size n = 114

    Sample mean X = 195

    Sample standard deviation σ = 73

    Confidence Interval (CI) 95 % means α = 5 % α/2 = 0,025

    Values from Z table for α/2 = 0,025

    Z = - 1,97 Z = 1,97

    Confidence Interval:

    CI X - Zα/2 * σ/√n ≤ x ≤ X - Zα/2 * σ/√n

    σ = 73 and n = 114

    73/√114 = 73/10,677 = 6,84

    CI 195 - (1,97) * 6,84 ≤ x ≤ 195 + (1,97) * 6,84

    195 - 13,47 ≤ x ≤ 195 + 13,47

    181,53 ≤ x ≤ 208,47

    According to rounding criteria

    182 ≤ x ≤ 208
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