8
QuizMultiple Choice

Cumulative Exam — Cumulative exam

Question 8 • Probability and Statistics with Applications Honors Sem-1-FL-1210300 (2024-2025)

Response time is an important statistic for measuring the effectiveness of a fire department, and is measured as the difference between the time a fire house receives a call and the time the first piece of fire equipment leaves the station. The response times for fire departments in a large city are found to have an approximately Normal distribution, with a mean of 4.5 minutes and a standard deviation of 1.2 minutes. What percentage of fire station response times are between 4 and 6 minutes?Find the z-table here.

Answer
A
37.7%
B
44.3%
C
55.7%
D
62.3%

Explanation

Convert each response time to a z-score using z = (time − mean) ÷ standard deviation. For 4 minutes, z = (4 − 4.5) ÷ 1.2 ≈ −0.42; for 6 minutes, z = (6 − 4.5) ÷ 1.2 = 1.25. The area between these z-scores is about 0.8944 − 0.3372 = 0.5572, or 55.7%. The correct choice is 55.7%.

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