This table lists commonly used Excel functions for each probability distribution covered in Chapter 4, with real-life student-related examples you can try in Excel.
| Distribution | Excel Function | Example |
|---|---|---|
| Chi-Squared | CHISQ.DIST(x, df, cumulative) | A statistics quiz has 3 questions. What is the probability a student's score falls below 6.63? =CHISQ.DIST(6.63, 3, TRUE) |
| Exponential | EXPON.DIST(x, lambda, cumulative) | Time between bus arrivals follows an exponential distribution with λ = 0.5. What's the probability the next bus arrives in under 2 minutes? =EXPON.DIST(2, 0.5, TRUE) |
| Gamma | GAMMA.DIST(x, alpha, beta, cumulative) | A student drinks energy drinks to stay awake. If the waiting time between caffeine effects follows Gamma(2, 2), what's the chance they feel alert in under 10 minutes? =GAMMA.DIST(10, 2, 2, TRUE) |
| Normal | NORM.DIST(x, mean, std_dev, cumulative) | Test scores in a class are normally distributed with mean 70 and SD 5. What is the probability a student scores below 75? =NORM.DIST(75, 70, 5, TRUE) |
| Lognormal | LOGNORM.DIST(x, mean, std_dev, cumulative) | Daily spending on snacks follows a lognormal distribution. What’s the probability a student spends under $5 if mean=1, SD=0.5? =LOGNORM.DIST(5, 1, 0.5, TRUE) |
| Weibull | WEIBULL.DIST(x, alpha, beta, cumulative) | A student’s headphones typically last 5 months on average. What’s the chance they fail before month 4? (α=2, β=5) =WEIBULL.DIST(4, 2, 5, TRUE) |
| Beta | BETA.DIST(x, alpha, beta, cumulative, A, B) | Probability a student finishes a project within 60% of the time (scaled between 0 and 1). Assume α=2, β=5. =BETA.DIST(0.6, 2, 5, TRUE, 0, 1) |
| Poisson | POISSON.DIST(x, mean, cumulative) | On average, 4 students arrive at the library each hour. What is the probability that 3 or fewer students show up in the next hour? =POISSON.DIST(3, 4, TRUE) |
| Binomial | BINOM.DIST(x, trials, prob, cumulative) | A student takes 5 multiple-choice questions, each with a 40% chance of guessing correctly. What’s the probability they get 2 or fewer correct? =BINOM.DIST(2, 5, 0.4, TRUE) |
| Uniform | Use formula: (x - a) / (b - a) | Class starts between 2:00 and 2:10 randomly. What’s the chance it starts before 2:06? =(6 - 0) / (10 - 0) |
| Standard Normal | NORM.S.DIST(z, cumulative) | A student’s Z-score is 1.2. What is the probability they are below average + 1.2 SD? =NORM.S.DIST(1.2, TRUE) |
| t-distribution | T.DIST(x, df, cumulative) | A student performs a t-test and gets t = 2.1, df = 10. What’s the left-tail p-value? =T.DIST(2.1, 10, TRUE) |
| F-distribution | F.DIST(x, df1, df2, cumulative) | Comparing two variances in lab data, with df1=2, df2=10. What is P(F ≤ 3)? =F.DIST(3, 2, 10, TRUE) |