Math Problem Statement

Scores on the SAT Mathematics test are believed to be Normally distributed. The scores of a simple random sample of five students who recently took the exam are 550, 620, 710, 520, and 480. What is a 80% confidence interval for m, the population mean score on the SAT Math test?

Group of answer choices

(456.7, 695.3)

(463.4, 688.6)

(489.5, 662.5)

(513.8, 638.2)

Solution

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Math Problem Analysis

Mathematical Concepts

Statistics
Confidence Interval
Normal Distribution

Formulas

Sample mean: \( \bar{x} = \frac{\Sigma x_i}{n} \)
Sample standard deviation: \( s = \sqrt{\frac{\Sigma (x_i - \bar{x})^2}{n-1}} \)
Confidence interval: \( \bar{x} \pm z^* \frac{s}{\sqrt{n}} \)

Theorems

Central Limit Theorem

Suitable Grade Level

Grades 11-12