Assess Probability of Heads in Coin Tosses
Overview
This question evaluates understanding of discrete and continuous probability concepts, specifically the binomial model for repeated Bernoulli trials and the normal distribution with standardization, testing core statistical reasoning and sensitivity to distribution parameters.
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Aug 4, 2025, 10:55 AM
Data Scientist
Onsite
Statistics & Math
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Probability with Coin Tosses and the Normal Distribution
Context
Onsite data scientist screening question assessing basic probability and distribution knowledge.
Questions
- A fair coin is tossed N times, with independent tosses. What is the probability of observing exactly k heads?
- How does your answer change if the coin is biased, with probability p of heads on each toss?
- Let X ~ N(μ, σ²). Derive P(a < X < b) and explain how to standardize a normal variable.
Hint
- Use the binomial probability mass function (pmf) for parts (1) and (2).
- Use the Z-score transformation to standardize a normal variable.
Solution
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