Math Problem Statement
The amount of time travellers at an airport spend with customs officers has a mean of μ =32 μ =32 seconds and a standard deviation of σ =11 seconds. For a random sample of 45 travellers, what is the probability that their mean time spent with customs officers will be:
Standard Normal Distribution Table
a. Over 30 seconds?
Round to four decimal places if necessary
b. Under 35 seconds?
Round to four decimal places if necessary
c. Under 30 seconds or over 35 seconds?
Round to four decimal places if necessary
Solution
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Math Problem Analysis
Mathematical Concepts
Statistics
Probability
Central Limit Theorem
Normal Distribution
Formulas
Standard Error (SE) = σ / √n
Z-score formula: z = (X - μ) / SE
Probability from Z-score using standard normal distribution table
Theorems
Central Limit Theorem
Suitable Grade Level
College-level Statistics or Advanced High School Statistics
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