Probability of something happening given the mean and the standard deviation.

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Discussion Overview

The discussion revolves around a practice problem involving the probability of hurricanes occurring in the Caribbean during hurricane season, specifically focusing on the application of statistical distributions (binomial, normal, and potentially Poisson) given the mean and standard deviation of the random variable representing the number of hurricanes.

Discussion Character

  • Exploratory
  • Technical explanation
  • Debate/contested
  • Mathematical reasoning

Main Points Raised

  • One participant suggests that the problem may be modeled using a binomial distribution, calculating parameters based on the mean and standard deviation.
  • Another participant proposes that the problem might assume a normal distribution due to the lack of information about trials, noting that the binomial assumption leads to an invalid probability.
  • A later reply indicates that the normal distribution may not be appropriate either, as it does not fit well with the discrete nature of the hurricane count.
  • One participant questions whether a Poisson distribution might be more suitable, as it avoids the numerical contradiction encountered with the binomial approach.

Areas of Agreement / Disagreement

Participants express differing views on the appropriate statistical distribution to apply, with no consensus reached on whether to use binomial, normal, or Poisson distributions for the problem.

Contextual Notes

Participants note limitations in the assumptions regarding the distributions, particularly the appropriateness of using a normal approximation for a discrete variable and the implications of the binomial model leading to an invalid probability.

DanielJackins
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I'm doing a practice problem for my upcoming midterm and am stuck on a question.

3. The number of hurricanes that occur in the caribbean during hurricane season is a random variable, where the mean number of hurricanes occurring is 8, or E(X) = 8, with a standard deviation of 2.83.
(a) Find the probability, that in any given hurricane season, the number of hurricanes in the caribbean will be greater than 4 and less than 12.

So I figured this follows a binomial distribution. Given that, I noted that E(X)= np = 8, and that SD(X) = sqrt(Var(X)) = sqrt(np(1-p)) = 2.83. Knowing that information, I solved for p in 2.83 = sqrt(np(1-p)) and subbed in np = 8, and eventually got p = -.0011125. Which must be wrong.(?)

I don't even know if I'm on the right track, or am making some silly mistake.
 
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Perhaps the problem wants you to assume the number of hurricanes is normally distributed since it didn't tell you anything about the "number of trials" = number of opportunities to made a random draw for a hurricane.

What you did is an interesting way of thinking about the problem and I wouldn't say it was "wrong". It's just that the conclusion it produces shows that the assumption of a binomial distribution doesn't work.

(It's also true that the assumption of a normal distribution doesn't really work since the number of hurricanes is a discrete variable and bounded below. However, the normal distribution is frequently applied as an approximation in situations where it can't really be the exact distribution.)
 
DanielJackins said:
I'm doing a practice problem for my upcoming midterm and am stuck on a question.

3. The number of hurricanes that occur in the caribbean during hurricane season is a random variable, where the mean number of hurricanes occurring is 8, or E(X) = 8, with a standard deviation of 2.83.
(a) Find the probability, that in any given hurricane season, the number of hurricanes in the caribbean will be greater than 4 and less than 12.

So I figured this follows a binomial distribution. Given that, I noted that E(X)= np = 8, and that SD(X) = sqrt(Var(X)) = sqrt(np(1-p)) = 2.83. Knowing that information, I solved for p in 2.83 = sqrt(np(1-p)) and subbed in np = 8, and eventually got p = -.0011125. Which must be wrong.(?)

I don't even know if I'm on the right track, or am making some silly mistake.

I haven't checked your math, but assume it is correct. I would assume that they want you to use the normal approximation to the binomial. If you've just been taught that, then I'm sure that's what it is. If you haven't been taught that, then I dunno.
 
You sure this isn't a Poisson question?
 
Pythagorean said:
You sure this isn't a Poisson question?
That's a good idea. It avoids a numerical contradiction and it is for a discrete random variable.
 

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