help probcalc-------------------------------------------------------------------------------

probcalc: Probability Calculator for Binomial, Poisson, and Normal Distributio> ns

probcalc{dist param1 param2 param3},param4 param5

Description:probcalc calculates the probability mass function for the discrete binomial and Poisson distributions and the probability density function for the continuous normal distribution. Output is written to the display in a format useful for learning probability calculations.

The algorithm can handle probability questions pertaining to, for example, "exactly 5 events," "at most 120 events," and "at least 7 events."

---------------------------------------------------------------------------

Commands for the Binomial Distribution:Probability of observing exactly x events, P(X=x)

probcalc b#n #pexactly#x} (Note: bold represents commands and #param represents actual numeric input value)The probability distribution based on n and p, densities only shown for pmf>0.01

probcalc b#n #pdistProbability of observing at most x events, P(X<=x)

probcalc b#n #patmost#xProbability of observing at least x events, P(X>=x)

probcalc b#n #patleast#x

Commands for the Poisson Distribution:Probability of observing exactly x events, P(X=x)

probcalc p#muexactly#xThe probability distribution based on mu, densities only shown for pmf>0.01

probcalc p#mudistProbability of observing at most x events, P(X<=x)

probcalc p#muatmost#xProbability of observing at least x events, P(X>=x)

probcalc p#muatleast#x

Commands for the Normal Distribution:Probability of observing a value of X between a and b, P(a<=X<b)

probcalc n#mean #sigmabetween#a #bThe probability density within plus-minus 4 standard deviations of a mean (30 bins)

probcalc n#mean #sigmadistProbability of observing an X-value that is at most x, P(X<=x)

probcalc n#mean #sigmaatmost#xProbability of observing an X-value that is at least x, P(X>=x)

probcalc n#mean #sigmaatleast#x

Examples:

A set of measurements for a particular variable follow the binomial distribution with parameters n=15 and p=0.15. What is the probability of occurrence of exactly 5 events, P(X=5)?

.probcalc b 15 0.15 exactly 5Generate the distribution of binomial variates based on the parameter values n=30 and p=0.35. What is the probability distribution, showing only variates for which pmf>0.01?

.probcalc b 30 0.35 distA variable was observed to follow the binomial distribution with n=100 and p=0.17. What is the probability of observing at most 16 events, P(X<=16)? (16 and less --> left tail)

.probcalc b 100 0.17 atmost 16Quark-gluon collisions were tabulated for a number of identical collider experiments and were found to follow a binomial distribution with n=1500 and p=0.25. What is the chance that at least 375 collisions would have been observed, P(X>=375)? (375 and greater --> right tail)

.probcalc b 1500 0.25 atleast 375An event occurs at a rate of mu=15 times per day on average. What is the probability of exactly 5 events occuring on any given day, P(X=5)?

.probcalc p 15 exactly 5What is the Poisson probability distribution when mu=10? (Note: only variates for which pmf>0.01 are shown)

.probcalc p 10 distAn event occurs on average mu=100 per millisecond. What is the probability of at most 93 events will be observed in a millisecond, P(X<=93)? (93 and less -> left tail)

.probcalc p 100 atmost 93The number of ions that interact within a square centimeter of target material is mu=14. What is the probability that at least 12 ions will interact in a square centimeter of area, P(X>=12)? (12 and greater --> right tail)

.probcalc p 14 atleast 12Daily caloric intake among a set of low-fat diet participants was found to be normally distributed with mean 1987 (calories) and s.d.=52. What proportion of participants would be expected to have daily caloric intake values between 1930 and 2040 calories, P(1930<X<=2040)?

.probcalc n 1987 52 between 1930 2040Patient weight measurements indicate a mean of 150 and s.d. of 20. What is the normal probability density between plus-minus 4 standard deviations of the mean?

.probcalc n 150 20 distWeight of high school students was determined to be normally distributed with mean=128 (lbs) and s.d.=25 (i.e., s.d.). What proportion of students are likely to weigh less than 120 lbs, P(X<=120)?

.probcalc n 128 25 atmost 120Daily temperature in Houston was determined to be normally distributed with mean=68 and s.d.=16. What is the chance of the temperature being 90F or greater, P(X>=90)?

.probcalc n 68 16 atleast 90

During run-time, output results merely displayed to the screen, for cutting and pasting.

Leif E. PetersonAssociate Professor of Public HealthWeill Cornell Medical College, Cornell UniversityCenter for Biostatistics, The Methodist Hospital Research Institute (TMHRI)Email:lepeterson@tmhs.org

Also seeOnline:

binomialp,binomial,poissonp,poisson,normal.