Math Problem Statement
A survey of the US population found that 26% of consumers shop for groceries online. Suppose you select a sample of 200 consumers. Using what you know about the distribution of the sample proportion answer the following question.
Suppose instead you take a sample of 800 consumers. What is the probability that between 23% and 29% of consumers in your sample shop for groceries online?
(Round answers 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
Statistics
Sampling Distribution
Normal Distribution
Probability
Formulas
Sample Proportion: p̂ = x / n
Standard Error: SE = sqrt[p(1-p)/n]
Z-score: Z = (p̂ - p) / SE
Probability Calculation using Normal Distribution
Theorems
Central Limit Theorem
Suitable Grade Level
Undergraduate Statistics
Related Recommendation
Probability Calculation for Online Grocery Shoppers Using Central Limit Theorem
Probability of Sample Proportion Spending More than $125 on Groceries
Calculate Probability of Sample Proportion Greater Than 75% with a Population Proportion of 67%
Constructing a 99% Confidence Interval for Population Proportion
Probability Calculation: Sample Proportion of First-Time Customers