Math Problem Statement
Determine whether you can use a normal distribution to approximate the binomial distribution. If you can, use the normal distribution to approximate the indicated probabilities and sketch their graphs. If you cannot, explain why and use a binomial distribution to find the indicated probabilities. Identify any unusual events. Explain. In a survey of U.S. college students, 62% said that if their college offers new programs tailored to the new economy, it will make them more likely to re-enroll. You randomly select 42 college students. Find the probability that the number who are more likely to enroll if their college offers new programs tailored to the new economy is (a) exactly 26, (b) at least 31, and (c) at most 25. Question content area bottom Part 1 Determine whether a normal distribution can be used to approximate the binomial distribution. Choose the correct answer. A. No, because npless than5. B. No, because nqless than5. C. Yes, because both npgreater than or equals5 and nqgreater than or equals5.
Solution
Ask a new question for Free
By Image
Drop file here or Click Here to upload
Math Problem Analysis
Mathematical Concepts
Probability
Binomial Distribution
Normal Approximation
Z-scores
Continuity Correction
Formulas
np = n × p
nq = n × (1 - p)
Mean (μ) = np
Standard Deviation (σ) = √(npq)
Z = (X - μ) / σ
Theorems
Central Limit Theorem
Suitable Grade Level
Grades 10-12
Related Recommendation
Using Normal Approximation to Solve a Binomial Distribution Problem in Probability
Probability Calculation for Students Needing Another Math Class Using Binomial Distribution
Probability of Correct Brand Identification in a Marketing Survey Using Binomial Distribution
Sampling Distribution and Normal Approximation for Population Proportion
Binomial Distribution: Probabilities of Americans Agreeing on College Education Importance