SSC CGL Statistics – Random Variables & Probability Distributions – Level 2 · Exam Level · Paper II Sprint

← Back

SSC CGL Statistics – Random Variables & Probability Distributions – Level 2 · Exam Level · Paper II Sprint – 15 questions, subject: Statistics (Tier II Paper II). Every question has the correct answer with a one-line explanation; tap "Show Answer". Free practice for TNPSC, UPSC, SSC, Bank and RRB exams – Shanmugam IAS Academy, Coimbatore.

Get daily current affairs & exam alerts – follow us YouTube WhatsApp Channel Telegram Channel Facebook Page Instagram
Share with friends & study groups
Link to this page from your website / blog (HTML code)
1.  
The mean and variance of a binomial distribution are 4 and 3 respectively. The number of trials n is:

Correct Answer: C [16]

Explanation:

q = variance/mean = 3/4, p = 1/4, n = mean/p = 16.

2.  
For a binomial distribution with n = 6, P(X = 1) = 0.393216 and P(X = 2) = 0.24576. The value of p is:

Correct Answer: B [1/5]

Explanation:

P(2)/P(1) = (5/2)(p/q) = 0.625 → p/q = 1/4 → p = 1/5.

3.  
For a Poisson variable X, 2P(X = 1) = P(X = 2). Then P(X = 0) is:

Correct Answer: A [0.0183]

Explanation:

2me⁻ᵐ = m²e⁻ᵐ/2 → m = 4 → P(0) = e⁻⁴ ≈ 0.0183.

4.  
1% of the bulbs made by a machine are defective. Using the Poisson approximation, the probability that a box of 200 bulbs has no defective bulb is:

Correct Answer: D [0.1353]

Explanation:

m = np = 200 × 0.01 = 2 → P(0) = e⁻² ≈ 0.1353.

5.  
X is normal with mean 50 and SD 5. P(X > 60) is:

Correct Answer: C [0.0228]

Explanation:

z = (60 − 50)/5 = 2 → P(Z > 2) = 1 − 0.9772 = 0.0228.

6.  
Heights of 2,000 men are normal with mean 165 cm and SD 6 cm. About how many are between 159 cm and 171 cm?

Correct Answer: D [About 1,365]

Explanation:

z from −1 to 1 → 0.6827 × 2,000 ≈ 1,365.

7.  
Two-quantity comparison
Quantity I: variance of a Poisson variable with mean 3
Quantity II: variance of a binomial variable with n = 12, p = 1/2

Correct Answer: A [Quantity I = Quantity II]

Explanation:

QI = m = 3; QII = npq = 12 × 1/2 × 1/2 = 3.

8.  
X and Y are independent with Var(X) = 4 and Var(Y) = 9. Var(2X − Y) is:

Correct Answer: B [25]

Explanation:

Var(2X − Y) = 4Var X + Var Y = 16 + 9 = 25 (variances add even for a difference).

9.  
Waiting time for a bus is exponential with mean 10 minutes. The probability of waiting more than 5 minutes is:

Correct Answer: C [0.6065]

Explanation:

P(X > x) = e −x/mean = e −0.5 ≈ 0.6065.

10.  
Assertion–Reason
A: A Poisson distribution with m = 4 has two modes, 3 and 4.
R: When m is a whole number, P(X = m − 1) = P(X = m).

Correct Answer: A [Both A and R are true and R explains A]

Explanation:

Ladder: P(m)/P(m − 1) = m/m = 1, so both values are highest.

11.  
Trick SpotterA binomial distribution has mean 12 and SD 3. The quickest first step to find n is:

Correct Answer: D [q = variance ÷ mean = 9/12]

Explanation:

q = 9/12 = 3/4 → p = 1/4 → n = 12 ÷ 1/4 = 48.

12.  
Spot My Mistake“X is Poisson with m = 16, so its standard deviation is 16.” The correct SD is:

Correct Answer: B [4]

Explanation:

Mean = variance = 16; SD = √16 = 4.

13.  
Reverse questionX is normal with mean 70, and 2.28% of the values exceed 90. The SD of X is:

Correct Answer: B [10]

Explanation:

Upper tail 0.0228 ↔ z = 2 → (90 − 70)/σ = 2 → σ = 10.

14.  
Diagram-basedThe bar chart shows the probability distribution of X.

E(X) is:

Correct Answer: C [2.7]

Explanation:

E(X) = 1(0.1) + 2(0.3) + 3(0.4) + 4(0.2) = 2.7.

15.  
The first two moments of a distribution about the value 3 are −1 and 7. The mean and variance are:

Correct Answer: D [Mean 2, variance 6]

Explanation:

Mean = 3 + (−1) = 2; μ₂ = μ₂′ − μ₁′² = 7 − 1 = 6.

➤ Full notes, shortcuts and every answer explained – SSC CGL 2026 Statistics (Tier II Paper II) book (₹149): www.shanmugamiasacademy.in/study-materials/ssc-cgl-statistics

📘 SSC CGL 2026 – Statistics (Tier II Paper II)
Here you get the answer with a one-line explanation. 657 original questions with worked answers · notes, formulas, figures and statistical tables (z, t, χ², F) · practice sets + 3 mock tests
Get the book – ₹149 ₹299 →
Score: 0 Answered: 0 / 0