UNIT II Assessment Questions

Assessment Questions Due : Feb 28.02.2025

Here are 2 assessment questions for each of the topics: Bernoulli, Binomial, Geometric, and Poisson distributions. These questions are practical, scenario-based, and ideal for testing understanding.

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1. Bernoulli Distribution

Question 1:
An engineer is testing the compressive strength of a concrete block. The probability that the block meets the required strength is $p = 0.8$.

• (a) What is the probability that the block fails to meet the required strength?
• (b) If the outcome is recorded as 1 for success and 0 for failure, what are the possible probabilities for $X$?

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Question 2:
A soil test is conducted to determine if the soil is fertile. The probability that the soil is fertile is $p = 0.6$.

• (a) What is the probability of finding infertile soil?
• (b) If 5 tests are conducted independently, how many tests are expected to return a positive result?

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2. Binomial Distribution

Question 1:
A batch of 10 steel rods is tested for defects. The probability that a rod is defective is $p = 0.1$.

• (a) What is the probability that exactly 3 rods are defective?
• (b) What is the probability that at least 2 rods are defective?

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Question 2:
In a quality control process, the probability of a brick being defective is $p = 0.05$. A sample of 20 bricks is inspected.

• (a) What is the probability that no brick is defective?
• (b) What is the probability that exactly 2 bricks are defective?

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3. Geometric Distribution

Question 1:
A geologist is testing rocks for mineral content. The probability of finding a rock with a high mineral content is $p = 0.3$.

• (a) What is the probability that the first high-mineral-content rock is found on the 4th test?
• (b) What is the probability that the first high-mineral-content rock is found on or before the 3rd test?

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Question 2:
A civil engineer is checking culverts to find one that meets the required specifications. The probability that a culvert meets specifications is $p = 0.4$.

• (a) What is the probability that the first suitable culvert is found on the 6th attempt?
• (b) What is the expected number of culverts the engineer needs to inspect before finding a suitable one?

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4. Poisson Distribution

Question 1:
Vehicles pass through a toll gate at an average rate of 6 per hour. The number of vehicles follows a Poisson distribution.

• (a) What is the probability that exactly 4 vehicles pass through the gate in a given hour?
• (b) What is the probability that more than 6 vehicles pass through the gate in an hour?

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Question 2:
In a rural area, landslides occur at an average rate of 3 per year. The number of landslides follows a Poisson distribution.

• (a) What is the probability of observing no landslides in a year?
• (b) What is the probability of observing at least 2 landslides in a year?

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These questions are tailored to test understanding and application of each distribution in civil engineering contexts. Let me know if you’d like solutions for any of these!