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.
这组 Wayfair OA 题目主要考查基础统计与概率：标准正态分布的均值与方差、已知并集与交集求条件概率、样本均值 / 样本标准差 / 中位数的计算、以及利用中心极限定理把和分布近似为正态分布。最后一道比较分数题本质上是看标准化后的相对表现，也就是比较 z-score，而不是直接比较原始分数；因此即使原始成绩不同，谁更接近自己所在分布的上层，谁的相对表现就更好。
