Approximate the Prob. in a normal distribution of a binomial

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SUMMARY

The discussion centers on the application of the Continuity Correction when approximating probabilities in a normal distribution derived from a binomial distribution. The user initially struggled with the correct application of this correction, leading to discrepancies in calculated probabilities. Specifically, the user reported a probability of 0.3264, while the book provided a value of 0.3974. It was clarified that the Continuity Correction should not be used when evaluating a probability for a continuous random variable, which contributed to the user's confusion and incorrect results.

PREREQUISITES
  • Understanding of binomial distributions
  • Familiarity with normal distribution approximations
  • Knowledge of the Continuity Correction concept
  • Basic probability theory
NEXT STEPS
  • Study the application of the Continuity Correction in probability distributions
  • Learn how to derive normal approximations from binomial distributions
  • Practice calculating exact probabilities for binomial distributions
  • Explore the differences between discrete and continuous random variables
USEFUL FOR

Students studying statistics, educators teaching probability theory, and anyone looking to understand the nuances of normal approximations in binomial distributions.

rogo0034
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Homework Statement


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The Attempt at a Solution


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See, i was having trouble determining when to use the Continuity Correction in the problems, and i guess i still am. but i was able to match my answer with the given one from the back of the book when I stopped using it. however, the second problem doesn't match, even after using the new formula and the new percentage.

I got .3264 and they got .3974

Where am i going wrong here? anyone?
 
rogo0034 said:
See, i was having trouble determining when to use the Continuity Correction in the problems, and i guess i still am. but i was able to match my answer with the given one from the back of the book when I stopped using it. however, the second problem doesn't match, even after using the new formula and the new percentage.

I got .3264 and they got .3974

Where am i going wrong here? anyone?

You should NOT use the continuity correction in (a), because you are NOT approximating a discrete distribution by a continuous one; you are evaluating a probability for a truly continuous random variable. So, you get a slightly wrong probability in (a), then you use that incorrect value in (b).

I get values different from yours and (presumably) from the book's. For (b) I get: exact probability = 0.374928, normal approx with continuity correction = 0.396911, normal approx without continuity correction = 0.472994.

RGV
 

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