# BARC Quiz 7: Solution and Q&A

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?

## Quiz 7 - Part 1

Solution | Problem |
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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? |

## Quiz 7 - Part 2

- 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?
- 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?
- 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?

## Quiz 7 - Part 3

- 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?
- Find $P(0 \lt z \lt 1.25)$, where $z$ has the standard normal distribution.
- 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.

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