Company: Bain_&_Company_MCQ
Difficulty: medium
The following pie-chart represents the sector-wise distribution of loans by the lender Housing Finance Corp. Total loans disbursed = Rs. 18,000 crores. Sector-wise Distribution (in degrees): Rubber: 10, Leather: 5, Jute: 15, Engineering: 70, Iron & Steel: 80, Software: 15, Sugar: 20, Electrical tools: 60, Textiles: 80, Others: 5. If 60% of loans disbursed to the iron and steel sector are given by
A sample of 100 items has a mean value of 250 and a standard deviation of 20. Construct a 95% confidence interval for the population mean (using z = 1.96), and determine whether the value 255 lies within the interval.
The following IQ scores were recorded for 30 undergraduate students: 119, 125, 152, 125, 134, 142, 142, 128, 137, 134, 137, 119, 139, 134, 140, 131, 125, 134, 155, 125, 134, 142, 128, 137, 137, 134, 125, 134, 139, 126. What is the percentage of students who have an IQ score of 125?
Consider the full rank linear model y = Xβ + ε with X ∈ R (n×p) (full column rank), y ∈ R n and the linear constraint Cβ = d, where C ∈ R (m×p) has full row rank and β̂ OLS denote the unconstrained OLS estimator. Which expression gives the unique constrained least-squares solution β̂ c (assume the constraint is feasible)?
A start-up claims that 60% of users who install its app remain active after one month. An investor adopts a beta (α=2, β=2) prior for the retention probability p. She observes that, out of 20 new installs, 9 are still active after one month. What is the value 0.668 in the context of the posterior distribution?
A company recorded daily outputs for 15 days. Known values for 12 days are: 148, 152, 149, 154, 165, 162, 147, 151, 157, 153, 155, and one other value. For all 15 days, the mean is 154 and the median is 155. The three missing outputs are distinct integers, exactly one is ≤154, and the other two are consecutive integers strictly greater than 155. The range of the full dataset is 20 units. Find the