High School

Noise levels at 77 concerts were measured in decibels, yielding the following data: 197, 141, 141, 152, 145, 187, 166, 197, 141, 141, 152, 145, 187, 166.

Construct the 80% confidence interval for the mean noise level at such locations, assuming the population is approximately normal.

Step 1 of 4: Calculate the sample mean for the given sample data. Round your answer to one decimal place.

Answer :

To calculate the sample mean for the given data, we will first sum up all the noise level values and then divide by the number of values.

Given data:
197, 141, 141, 152, 145, 187, 166, 197, 141, 141, 152, 145, 187, 166

Step-by-step calculation:

  1. Sum of the values:
    First, we add all the numbers together. Here’s how it breaks down:

    [tex]197 + 141 + 141 + 152 + 145 + 187 + 166 + 197 + 141 + 141 + 152 + 145 + 187 + 166[/tex]
    = 2158

  2. Count of values:
    There are 14 noise levels provided in the data set.

  3. Calculate the Mean:
    The sample mean is computed using the formula:

    [tex]\text{Mean} = \frac{\text{Sum of all values}}{\text{Number of values}}[/tex]

    Substituting the values:

    [tex]\text{Mean} = \frac{2158}{14} \approx 154.1[/tex]

So, the sample mean of the noise level is approximately 154.1 decibels.

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