Math Problem Statement

A drug test is accurate 98% of the time. If the test is given to 1700 people who have not taken drugs, what is the probability that at least 37 will test positive?

Probability =

Give your answers to at least 3 decimal places.

Solution

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Math Problem Analysis

Mathematical Concepts

Binomial Distribution
Normal Approximation
Probability

Formulas

Mean (μ) = n * p
Standard Deviation (σ) = sqrt(n * p * (1 - p))
Z-score = (x - μ) / σ
Continuity correction for normal approximation

Theorems

Central Limit Theorem (for normal approximation of binomial distribution)

Suitable Grade Level

Undergraduate Level