High School

A study of 40 bowlers showed that their average score was 186. The standard deviation of the population is 6. Find the 95% confidence interval of the mean score for all bowlers.

A. 186 ± 1.96 * 6
B. 186 ± 2.58 * 6
C. 186 ± 3.29 * 6
D. 186 ± 4.20 * 6

Answer :

Final answer:

To find the 95% confidence interval of the mean score for all bowlers, use the formula: mean ± (z-score * (standard deviation / square root of sample size)). The correct answer is (A) 186 ± 1.96 * 6.

Explanation:

To find the 95% confidence interval of the mean score for all bowlers, we need to use the formula: mean ± (z-score * (standard deviation / square root of sample size)).

The z-score for a 95% confidence level is 1.96.

Substituting the given values, the 95% confidence interval is: 186 ± (1.96 * (6 / √40)).

Simplifying the expression gives us the answer: 186 ± 1.55.

Therefore, the correct answer is (A) 186 ± 1.96 * 6.

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