Math Problem Statement
A marketing survey is conducted in which students are to taste two different brands of soft drink. Their task is to correctly identify the brand tasted. A random sample of 200 students is taken. Assume that the students have no ability to distinguish between the two brands. Complete (a) through (c) below.
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Part 1
a. What is the probability that the sample will have between 50% and 60% of the identifications correct? (Round to four decimal places as needed.)
Solution
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Math Problem Analysis
Mathematical Concepts
Binomial Probability Distribution
Normal Approximation to Binomial
Z-scores
Formulas
Mean: μ = np
Standard deviation: σ = sqrt(np(1-p))
Z-score: z = (X - μ) / σ
Theorems
Central Limit Theorem
Suitable Grade Level
Grades 10-12 (Advanced High School)
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