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When the event of interest is a cumulative event.
For example, to find the probability of getting three Heads in 8 tosses of a fair coin you would use the regular binomial distribution. But to find the probability of up to 3 Heads you would use the cumulative distribution.
This is because
Prob("up to 3") = Prob(0 or 1 or 2 or 3) = Prob(0) + Prob(1) + Prob(2) + Prob(3) since these are mutually exclusive.
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The probability that an individual is left handed is 0.1 In a class of 30 students what is the probability of finding at least 5 left hander's?
This is a binomial probability distribution. The number of trials, n, equals 30; and the probability of success is p, which is 0.1. In this problem, you want the probability of at least 5, which is the complement of at most 4. We use the complement because we can subtract from 1 that probability and we will have the solution. The related link has the binomial probability distribution table which is cumulative. Per the table, at n=30, p=0.1 and x = 4; the probability is 0.825. Therefore the probability of at least 5 is 1 - 0.825 or 0.175.
The mean of a binomial probability distribution can be determined by multiplying?
The mean of a binomial probability distribution can be determined by multiplying the sample size times the probability of success.
What is the symbol for probability of success in a binomial trial?
The symbol for probability of success in a binomial trial is the letter p. It is the symbol used for probability in all statistical testing.
The probability of a single hazard occurring is?
proportional to the cumulative probability of all the causes listed for that hazard
Can you use the formulas for a probability distribution to calculate parameters for a binomial probability distribution or can you just use the given formulas for a binomial probability distribution?
This depends on what information you have. If you know the success probability and the total number of observations, you can use the given formulas. Most of the time, this is the case. If you have data or experience which allow you to estimate the parameters, it may sometimes happen that you work like this. This mostly happens when n is very large and p very small which results in an approximation with the Poisson distribution.
