Chapter Exam

Chapter 10: Probability Distributions — Online MCQ Test

Q: In a binomial distribution, what does the parameter \u201cn\u201d represent?

Answer: B. Number of trials — In a binomial distribution, n denotes the fixed number of independent trials. The probability of success is denoted by p.

Q: Which of the following is the formula for the probability mass function of a binomial distribution?

Answer: C. P(X=x)=nCx p^x q^(n-x) — The binomial probability formula is P(X=x)=nCx p^x q^(n-x), where q=1-p. It gives the probability of exactly x successes in n trials.

Q: A coin is tossed 5 times. What is the probability of getting exactly 2 heads?

Answer: B. 10/32 — This is a binomial situation with n=5 and p=1/2. The probability is 5C2(1/2)^2(1/2)^3 = 10/32.

Q: A binomial distribution has n = 10 and p = 0.3. What is its mean?

Answer: A. 3 — The mean of a binomial distribution is np. Here, np = 10 \u00d7 0.3 = 3.

Q: A machine produces items with a defect probability of 0.1. In 8 items, what is the probability of at least one defective item?

Answer: A. 1 - (0.9)^8 — The probability of at least one defective item is 1 minus the probability of no defective items. Since each item is good with probability 0.9, the answer is 1-(0.9)^8.

STATISTICS · CLASS 11th · Tamil Nadu State Board

Practice Chapter 10: Probability Distributions with a free chapter-wise online MCQ test for Tamil Nadu State Board CLASS 11th STATISTICS. This chapter covers: The final chapter details theoretical probability distributions including Binomial Poisson and Normal distributions. Students study distribution properties parameters probability c.... AI-generated questions from basic to board-exam level, with instant results and explanations.

Questions

20m

Time Limit

Attempts Left

10 random questions from this chapter (mixed difficulty)
Questions you've seen before won't repeat until the pool resets
You have 20 minutes — exam auto-submits when time is up
Maximum 3 attempts per chapter
Results and explanations shown immediately after submission

New here? Register free — includes 3 free chapter exams.

Chapter 10: Probability Distributions — Important Questions & Answers (FAQ)

Frequently asked questions from Tamil Nadu State Board CLASS 11th STATISTICS — Chapter 10: Probability Distributions, with answers and explanations. These are sample questions; the exam has its own separate question set.

In a binomial distribution, what does the parameter \u201cn\u201d represent?

A. Probability of success in one trial
B. Number of trials ✓
C. Mean of the distribution
D. Standard deviation of the distribution

Answer: B. Number of trials
In a binomial distribution, n denotes the fixed number of independent trials. The probability of success is denoted by p.

Which of the following is the formula for the probability mass function of a binomial distribution?

A. P(X=x)=e^-\u03bb \u03bb^x / x!
B. P(X=x)=1/(\u03c3\u221a2\u03c0)e^(-(x-\u03bc)^2/2\u03c3^2)
C. P(X=x)=nCx p^x q^(n-x) ✓
D. P(X=x)=x/n

Answer: C. P(X=x)=nCx p^x q^(n-x)
The binomial probability formula is P(X=x)=nCx p^x q^(n-x), where q=1-p. It gives the probability of exactly x successes in n trials.

A coin is tossed 5 times. What is the probability of getting exactly 2 heads?

A. 5/16
B. 10/32 ✓
C. 1/2
D. 2/5

Answer: B. 10/32
This is a binomial situation with n=5 and p=1/2. The probability is 5C2(1/2)^2(1/2)^3 = 10/32.

A binomial distribution has n = 10 and p = 0.3. What is its mean?

A. 3 ✓
B. 7
C. 0.3
D. 10.3

Answer: A. 3
The mean of a binomial distribution is np. Here, np = 10 \u00d7 0.3 = 3.

A machine produces items with a defect probability of 0.1. In 8 items, what is the probability of at least one defective item?

A. 1 - (0.9)^8 ✓
B. (0.1)^8
C. 8(0.1)(0.9)^7
D. 1 - (0.1)^8

Answer: A. 1 - (0.9)^8
The probability of at least one defective item is 1 minus the probability of no defective items. Since each item is good with probability 0.9, the answer is 1-(0.9)^8.