Math Problem Statement
The time spent commuting from home to work for all employees at a very large company has a normal distribution with a mean of 158 minutes and a standard deviation of 7 minutes. Determine the probability that the mean time spent commuting by a random sample of 99 employees is between 157.71 minutes and 160.31 minutes. 00.1937 0 0.527 00.6594 0 0.3401
Solution
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Math Problem Analysis
Mathematical Concepts
Normal Distribution
Sampling Distribution of the Mean
Probability
Formulas
Standard Error of the Mean (SEM): SEM = σ / √n
Z-score formula: z = (X - μ) / SEM
Probability of a range in a normal distribution
Theorems
Central Limit Theorem
Suitable Grade Level
Undergraduate Statistics or Advanced High School Statistics
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