BARC Quiz 7: Solution and Q&A

Contents

  1. Quiz 7 - Part 1
  2. Quiz 7 - Part 2
  3. Quiz 7 - Part 3

 

 

The probability that a patient recovers from a rare blood disease is 0.4. If 15 people are known to have contracted this disease, what is the probability that at least 10 survive?
 

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Quiz 7 - Part 1

Solution Problem
The number of cars passing a point on a road during a five-minute period may be modelled by the Poisson distribution with parameter 4. Find the probability that in five-minute period, fewer than 3 cars go past.
The probability that a certain kind of component will survive a given shock test is 3/4. Find the probability that exactly 2 of the next 4 components tested survive.
A large chain retailer purchases a certain kind of electronic device from a manufacturer. The manufacturer indicates that the defective rate of the device is 3%. Suppose that the retailer receives 10 shipments in a month and the inspector randomly tests 20 devices per shipment. What is the probability that there will be 3 shipments containing at least one defective device?

 

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Quiz 7 - Part 2

  1. If queries sent to a search engine arrive every 15 seconds on the average, what is the probability of waiting less than or equal to 30 seconds?
  2. The length of a telephone conversation is 2.5 minutes on average. What is the probability that a conversation lasts between 3 and 5 minutes?
  3. The length of a telephone conversation is 2.5 minutes on average. What is the probability that a conversation lasts between 3 and 5 minutes?

 

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Quiz 7 - Part 3

  1. Suppose a population is normally distributed with a mean of 24.6 and a standard deviation of 1.3. What percentage of data will lie between 25.3 and 26.8?
  2. Find $P(0 \lt z \lt 1.25)$, where $z$ has the standard normal distribution.
  3. An electrical firm manufactures light bulbs that have a length of life that is approximately normally distributed, with mean equal to 800 hours and a standard deviation of 40 hours. Find the probability that a random sample of 16 bulbs will have an average life of less than 775 hours.

 

Use the comment section below if you have any question and if you need some clarification.
 

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