Probability Distributions Quiz

Grade 11 · Math · Quiz

Test your knowledge of binomial and normal distributions, expected value, and probability calculations.

Questions

1. What is P(X = 3) for a binomial distribution with n = 5 and p = 0.4?

   1. 0.2304
   2. 0.3456
   3. 0.1536
   4. 0.0768
   Show answer

   Answer: 0.2304

   P(X=3) = C(5,3)(0.4)^3(0.6)^2 = 10 * 0.064 * 0.36 = 10 * 0.02304 = 0.2304.

2. A normal curve has μ = 100 and σ = 15. Approximately what percentage of values fall between 70 and 130?

   1. 68%
   2. 95%
   3. 99.7%
   4. 50%
   Show answer

   Answer: 95%

   70 = μ - 2σ and 130 = μ + 2σ; by the empirical rule, 95% of values fall within 2σ of the mean.

3. Which statement best describes a continuous probability distribution?

   1. Probabilities are assigned to individual points
   2. The probability of any exact value is 0
   3. All values in the range have equal probability
   4. The mean always equals the median
   Show answer

   Answer: The probability of any exact value is 0

   For continuous distributions, the probability of any exact single value is 0; probabilities are found over intervals.

4. If Z is standard normal and P(Z < z) = 0.9772, what is z?

   1. 1.0
   2. 1.5
   3. 2.0
   4. 2.5
   Show answer

   Answer: 2.0

   P(Z < 2.0) ≈ 0.9772 is a standard normal table value corresponding to z = 2.0.

5. A discrete random variable X has E(X) = 3 and E(X²) = 13. What is Var(X)?

   1. 4
   2. 10
   3. 2
   4. 13
   Show answer

   Answer: 4

   Var(X) = E(X²) - [E(X)]² = 13 - 9 = 4.

6. In 10 free throw attempts with a 70% success rate, what is the expected number of made shots?

   1. 5
   2. 6
   3. 7
   4. 8
   Show answer

   Answer: 7

   E(X) = np = 10 * 0.70 = 7.

7. The sum of all probabilities in a valid discrete probability distribution must equal 1.

   Show answer

   Answer: True

   This is a fundamental axiom of probability; all P(X=x) values must be non-negative and sum to 1.

8. For a standard normal distribution, the mean is 0 and the standard deviation is ___.

   Show answer

   Answer: 1

   The standard normal distribution N(0,1) has mean μ=0 and standard deviation σ=1 by definition.

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