On 06-Nov-10 11:16:28, Jumlong Vongprasert wrote: > Dear All > I have some problem with calculate probability. > Assume I have data with normal distribution with mean = 5 sd = 2. > I want to approximate probability = 2.4. > I used pnorm(2.4, 5, 2) - pnorm(2.4, 5, 2, lower.tail = FLASE), > correct or not. > Many Thanks > Jumlong
[A] Not correct because "FLASE" should be "FALSE". [B] Not correct because a) pnorm(2.4, 5, 2) is the probability that a value from a Normal distribution with mean 5 will be less than 2.4, and this is less than 1/2 (since 2.4 is less than the mean). b) pnorm(2.4, 5, 2, lower.tail = FALSE) is the probability that such a value will be greater than 2.4, and this is greater than 1/2 (for the same reason. c) The difference will therefore be (< 1/2) - (> 1/2) which will be less than 0, so cannot be a probability. [C] Not correct because a value sampled from a Normal distribution (which is a continuous distribution) has probability 0 of being exactly equal to any given value (e.g. 2.4); so I think your question does not express what you want to know. One possibility which could make your question realistic is that the value "2.4" that you are interested in is a value sampled from Normal(mean=5, sd=2) **that has been rounded to 1 decimal place** and so could have been any value between 2.35 and 2.45; in that case it makes sense to ask what is the probability of a value in this range from Normal(mean=5, sd=2). This would be pnorm(2.45, 5, 2) - pnorm(2.35, 5, 2) = 0.008569045 Of course, the degree of rounding may be different -- for example rounding to *even* values of the first decimal place, i.e. to values ... , 2.0, 2.2, 2.4, 2.6, 2.8, ... in which case the event whose probability you want is that the sampled value is between 2.3 and 2.5, whose probability is pnorm(2.5, 5, 2) - pnorm(2.3, 5, 2) = 0.01714178 Since the question you are really interested in cannot be identified from what you have asked (see examples above), you should try to make your question clear and definite! Hoping this helps, Ted. -------------------------------------------------------------------- E-Mail: (Ted Harding) <[email protected]> Fax-to-email: +44 (0)870 094 0861 Date: 06-Nov-10 Time: 12:06:17 ------------------------------ XFMail ------------------------------ ______________________________________________ [email protected] mailing list https://stat.ethz.ch/mailman/listinfo/r-help PLEASE do read the posting guide http://www.R-project.org/posting-guide.html and provide commented, minimal, self-contained, reproducible code.
