Math Problem Statement
Below,
n
is the sample size, p
is the population proportion of successes, and X
is the number of successes in the sample. Use the normal approximation and the Cumulative Normal Distribution Table to find the probability. Round the answer to at least four decimal places.=
n
=
78
,
p
0.43
P
<
X
40
Solution
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Math Problem Analysis
Mathematical Concepts
Statistics
Normal Approximation
Binomial Distribution
Z-scores
Continuity Correction
Formulas
Mean (μ) = np
Standard deviation (σ) = √(np(1 - p))
Z-score formula: z = (X - μ) / σ
Theorems
Normal Approximation to the Binomial Distribution
Continuity Correction
Standard Normal Distribution
Suitable Grade Level
Grades 11-12 or college-level statistics
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