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#157easyStatistics

Confidence Interval for Mean

Time Limit: 2sMemory: 256MB
Part of:Statistics & Distributions → Confidence Intervals

Problem

Given a sample of n values and a confidence level (as a percentage), compute the confidence interval for the population mean.

Use the sample mean, sample standard deviation, and the z-value corresponding to the confidence level.

Input Format

  • Line 1: integer n
  • Line 2: n space-separated floating-point values
  • Line 3: confidence level (e.g., 95)

Output Format

Two space-separated values: lower upper, each to 4 decimal places.

Examples

Example 1
Input(Line 1: integer n)
5
10 12 14 16 18
95
Output
11.2282 16.7718

Mean = 14, s = 3.1623, z = 1.96, margin = 1.96 * 3.1623 / sqrt(5) = 2.7718.

Example 2
Input(Line 1: integer n)
6
5 7 9 11 13 15
90
Output
7.4874 12.5126

Mean = 10, s = 3.7417, z = 1.6449, margin = 1.6449 * 3.7417 / sqrt(6) = 2.5126.

Constraints

  • •2 <= n <= 10000
  • •Values are floating-point numbers in [-10000, 10000]
  • •Confidence level is one of 80, 90, 95, or 99
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