The number of birth defects in a region is commonly modeled as having a binomial distribution, with a rate of four birth defects per 100 births considered a typical rate in the United States. What is the probability that a county that had 200 births during the year would have between 4 and 12 birth defects. Use both the binomial distribution and the Normal approximation with the appropriate continuity correction from the table below. Is the normal approximation reasonable?

College Algebra
7th Edition
ISBN:9781305115545
Author:James Stewart, Lothar Redlin, Saleem Watson
Publisher:James Stewart, Lothar Redlin, Saleem Watson
Chapter9: Counting And Probability
Section9.3: Binomial Probability
Problem 2E: If a binomial experiment has probability p success, then the probability of failure is...
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The number of birth defects in a region is commonly modeled as having a binomial distribution, with a rate of four birth defects per 100 births considered a typical rate in the United States. What is the probability that a county that had 200 births during the year would have between 4 and 12 birth defects. Use both the binomial distribution and the Normal approximation with the appropriate continuity correction from the table below. Is the normal approximation reasonable?
Binomial Distribution
P(x = 10)
P(x > 10)
P(x <= 10)
P(x = c)
P(x > c)
P(x <= c)
P(x<c)
P(x >= c)
P(a<x< b)
P(x < 10)
P(x >= 10)
P(9<x<11)
Normal Approximation
P(9.5<x< 10.5)
P(x > 10.5)
P(x < 10.5)
P(c-0.5<x<c+0.5)
P(x > c +0.5)
P(x<c+0.5)
P(x<c-0.5)
P(x < 9.5)
P(x > c-0.5)
P(x > 9.5)
P(a -0.5 < x < b +0.5) P(8.5<x< 11.5)
Notes
Includes c
Does not include c
Includes c
Does not include c
Includes c
Transcribed Image Text:Binomial Distribution P(x = 10) P(x > 10) P(x <= 10) P(x = c) P(x > c) P(x <= c) P(x<c) P(x >= c) P(a<x< b) P(x < 10) P(x >= 10) P(9<x<11) Normal Approximation P(9.5<x< 10.5) P(x > 10.5) P(x < 10.5) P(c-0.5<x<c+0.5) P(x > c +0.5) P(x<c+0.5) P(x<c-0.5) P(x < 9.5) P(x > c-0.5) P(x > 9.5) P(a -0.5 < x < b +0.5) P(8.5<x< 11.5) Notes Includes c Does not include c Includes c Does not include c Includes c
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