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.

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