Math Problem Statement
Employees at a regional hospital spend an average of $6 per day on lunch, with a standard deviation $4. A simple random sample of 100 employees is studied.
(a)
What is the expected value of the sampling distribution of the sample mean?
$
What is the standard deviation of the sampling distribution of the sample mean? (Round your answer to the nearest cent.)
$
What is the shape of the sampling distribution of the sample mean?
skewed to the rightexponential uniformskewed to the leftnormal
(b)
What is the probability that the sample mean will be at least $5.00? (Round your answer to four decimal places.)
(c)
What is the probability that the sample mean will be at least $6.50? (Round your answer to four decimal places.)
Solution
Ask a new question for Free
By Image
Drop file here or Click Here to upload
Math Problem Analysis
Mathematical Concepts
Sampling Distribution
Central Limit Theorem
Normal Distribution
Z-scores
Probability
Formulas
Expected value of sample mean: μ_x̄ = μ
Standard deviation of sample mean: σ_x̄ = σ / √n
Z-score formula: z = (x - μ) / σ
Theorems
Central Limit Theorem
Suitable Grade Level
Grades 10-12 (Advanced High School Statistics or Introductory College-Level Statistics)
Related Recommendation
Calculating Probabilities for Sample Means Using the Central Limit Theorem
Normal Distribution Probability for Sample and Population - Mean μ = 33.2, Standard Deviation σ = 68.9
Sampling Distribution and Probability Calculations for Skewed Populations
Probability of Production Costs using Normal Distribution
Probability Calculations for Change Carried by Statistics Students Using Normal Distributions