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rogo0034
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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?
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.
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.
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.
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.
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.