1. Standard Normal Distribution
For a standard normal distribution, what are its mean and variance?
Pick ONE option.
2. Probability – II
In a family, the probability that at least one parent falls ill is 20%. If the probability that the father falls ill is 12% and the probability that both the parents fall ill is 5%, what is the probability that the mother falls ill?
Pick ONE option.
3. Sample Mean, Standard Deviation and Median
The following data is from a random sample: 7, 7, 9, 13, 10. Compute the sample mean, sample standard deviation, and sample median.
Pick ONE option.
4. Central Limit Theorem (CLT)
Let X1, X2, ..., X75 be i.i.d., each with expected value μ = E(Xi) = 2 and variance σ² = Var(Xi) = 3. Approximate P(X1 + X2 + ··· + X75 > 120) using the central limit theorem. For the solution, it can be assumed that P(|Z| < 2) ≈ 0.95, where Z is a random variable that has a standard normal distribution.
Pick ONE option.
5. Compare Scores
A student received the following marks for exams in 2 subjects. Which subject showed better relative performance? (Assume scores follow a normal distribution.)
- Maths: marks =
70, mean =60, standard deviation =15 - Science: marks =
72, mean =68, standard deviation =6
Pick ONE option.
This Wayfair OA set focuses on core statistics and probability concepts: the standard normal distribution, set-based probability relationships, sample mean/standard deviation/median, and the central limit theorem for approximating a sum by a normal distribution. The final score-comparison question is a z-score problem in disguise, where relative performance should be judged by standardizing each mark against its subject mean and standard deviation rather than comparing raw scores directly.
