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 36 students in the high school and found a mean of 156 messages sent per day with a standard deviation of 61 messages. Determine a 95% confidence interval for the mean, rounding all values to the nearest whole number.

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Identify Data: Identify the sample mean (x̄), sample size (n), and sample standard deviation (s). The sample mean (x̄) is given as 156 messages. The sample size (n) is given as 36 students. The sample standard deviation (s) is given as 61 messages.Calculate SEM: Determine the standard error of the mean (SEM). The standard error of the mean is calculated using the formula SEM = s / √n. SEM = 61 / √36 SEM = 61 / 6 SEM = 10.17 We round this to the nearest whole number, which is 10.Find Critical Value: Find the critical value for a 95% confidence interval. Since the sample size is greater than 30, we can use the z-distribution. For a 95% confidence interval, the z-score is typically 1.96.Calculate ME: Calculate the margin of error (ME). The margin of error is calculated using the formula ME = z * SEM. ME = 1.96 * 10 ME = 19.6 We round this to the nearest whole number, which is 20.Determine Confidence Interval: Determine the confidence interval. The confidence interval is calculated using the formula: (x̄ - ME, x̄ + ME). Lower bound = 156 - 20 Lower bound = 136 Upper bound = 156 + 20 Upper bound = 176State Final Answer: State the final answer. The 95% confidence interval for the mean number of text messages sent per day by students is (136, 176).

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