Probability Distributions and basic Statistics appear in CUET Section B2 at the conceptual and formula-application level — not at the deep computation level. That means if you know the correct formula and when to use it, you can answer most of these questions in under a minute.

This post covers exactly that: what each distribution looks like, when to use it, and what CUET actually tests.

How to Identify Which Distribution to Use

Before looking at the formulas, train yourself to recognise the type of distribution from the question’s language.

Signal in the questionDistribution to use
"n trials", "probability of success p", "how many successes"Binomial
"rare events", "per unit time/area/interval"Poisson
"normally distributed", "mean and SD given", "standardise"Normal

Get this right first — then apply the formula.

1. Binomial Distribution

When to use: A fixed number of independent trials ($n$), each with the same probability of success ($p$).

X∼Bin(n,p)X \sim \text{Bin}(n, p)

Key Formulas

Mean=np\text{Mean} = np
Variance=npqwhere q=1−p\text{Variance} = npq \quad \text{where } q = 1 - p
Standard Deviation=npq\text{Standard Deviation} = \sqrt{npq}

What CUET Tests

Most CUET Binomial questions ask for the mean or variance directly — straight substitution into the formulas above.

Example: $X \sim \text{Bin}(20, 0.1)$

Mean=20×0.1=2\text{Mean} = 20 \times 0.1 = \mathbf{2}
Variance=20×0.1×0.9=1.8\text{Variance} = 20 \times 0.1 \times 0.9 = \mathbf{1.8}

Memory hook: Mean = np (think “n trials, p chance each”). Variance adds the $q$ factor.

2. Poisson Distribution

When to use: Counting the number of times a rare event occurs in a fixed interval of time, space, or length.

X∼Poisson(λ)X \sim \text{Poisson}(\lambda)

Key Formulas

Mean=λ\text{Mean} = \lambda
Variance=λ\text{Variance} = \lambda

The most memorable fact about Poisson: mean equals variance. If a question gives you both and they’re equal, it’s Poisson.

Recognising Poisson in CUET

Look for:

  • Number of calls received per hour

  • Number of defects per unit of fabric

  • Number of accidents per day on a highway

  • Any “rate of occurrence” scenario

3. Normal Distribution

When to use: Continuous data that is symmetric and bell-shaped around a mean.

Z=X−μσZ = \frac{X - \mu}{\sigma}

This converts any normally distributed variable into the standard normal (mean = 0, SD = 1).

What CUET Tests at This Level

CUET Applied Mathematics does not require you to read Z-tables in depth. The questions focus on:

  1. Standardisation — calculating the Z-score from given $X$, $\mu$, $\sigma$

  2. Conceptual properties — symmetry, the mean/median/mode being equal, area under the curve

  3. Identifying the correct formula — from answer options

Key Properties to Remember

PropertyValue
Mean = Median = ModeAlways true for normal distribution
Total area under curve1 (or 100%)
Area within ±1 SD≈ 68%
Area within ±2 SD≈ 95%
Area within ±3 SD≈ 99.7%

4. Descriptive Statistics (Quick Reference)

These appear throughout Section B2 — often as direct formula-substitution questions.

Measures of Central Tendency

xˉ=∑xn\bar{x} = \frac{\sum x}{n}

Variance and Standard Deviation

Variance=∑(x−xˉ)2n\text{Variance} = \frac{\sum (x - \bar{x})^2}{n}
SD=Variance\text{SD} = \sqrt{\text{Variance}}

Fast MCQ Elimination Rules

  • SD can never be negative — eliminate any option < 0 immediately

  • Variance can never be negative — same rule

  • If all values are identical, SD = 0

  • A single outlier raises both variance and SD significantly

Side-by-Side: The Three Distributions

FeatureBinomialPoissonNormal
Data typeDiscreteDiscreteContinuous
Trigger phrase"n trials, p success""rare events per interval""normally distributed"
Mean$np$$\lambda$$\mu$
Variance$npq$$\lambda$$\sigma^2$
Special propertyMean ≠ Variance (usually)Mean = VarianceSymmetric bell curve

Quick Practice MCQ

Q. If $X \sim \text{Bin}(20, 0.1)$, the mean of X is:

  • A) 0.2 B) 2 ✓ C) 10 D) 18

Mean = np = 20 × 0.1 = 2

Q. Which distribution would you use to model the number of customer complaints received per day at a call centre?

  • A) Binomial B) Normal C) Poisson ✓ D) Uniform

Rate of rare events per interval → Poisson

What’s Next?

In Part 4, put everything together with the full Applied Mathematics MCQ practice set — 6 questions across Financial Maths, Numbers & Quantification, and Distributions, each with a worked solution and the exact reasoning strategy to use.