Approximate the Prob. in a normal distribution of a binomial

• rogo0034
In summary, the conversation discusses the use of the Continuity Correction in probability problems. The person had trouble determining when to use it and was able to match their answer with the book's when they stopped using it. However, in the second problem, their answer did not match. Further discussion reveals that the Continuity Correction should not be used in this case, and the correct probabilities are different from the book's answer.
rogo0034

The Attempt at a Solution

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

1. What is the difference between a normal distribution and a binomial distribution?

A normal distribution is a continuous probability distribution that follows a bell-shaped curve and is often used to model natural phenomena. A binomial distribution, on the other hand, is a discrete probability distribution that models the number of successes in a fixed number of independent trials. In other words, a normal distribution represents continuous data while a binomial distribution represents discrete data.

2. How do you approximate the probability in a normal distribution of a binomial?

To approximate the probability in a normal distribution of a binomial, you can use the central limit theorem. This theorem states that as the sample size increases, the sample mean of a binomial distribution will approach a normal distribution. This allows you to use the mean and standard deviation of the binomial distribution to calculate probabilities using a normal distribution table or a statistical software.

3. What is the formula for approximating the probability in a normal distribution of a binomial?

The formula for approximating the probability in a normal distribution of a binomial is:
P(X ≤ x) = Φ((x + 0.5 – np)/√(npq)), where x is the number of successes, n is the number of trials, p is the probability of success, and q is the probability of failure.

4. Can you approximate the probability in a normal distribution of a binomial for any sample size?

Yes, the central limit theorem allows you to approximate the probability in a normal distribution of a binomial for any sample size. However, for smaller sample sizes, the approximation may not be as accurate.

5. How do you determine if a binomial distribution can be approximated by a normal distribution?

A binomial distribution can be approximated by a normal distribution if the sample size is large enough (usually greater than 30) and the probability of success is not too close to 0 or 1. You can also visually check if the data follows a bell-shaped curve, which is characteristic of a normal distribution.

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