For each problem:a) Identify whether the best distribution to solve the problem is Binomial, Poisson, or Exponential.b) Identify the correct value of all associated parameters.c) Find the indicated probability to 4 decimal places. ### Probability Problems:**Problem 6:**"A certain kind of light bulb lasts 1 year on average. What is the probability that a given light bulb will fail in less than a year?"**Problem 7:**"Suppose that the expected number of customers at a convenience store is 5 every 20 minutes. In a given 20-minute time period, find the probability of having more than 3 customers."**Problem 8:**"Find the probability that an investor makes a profit on 6 of her next 12 investments, assuming independence and a 0.6 chance of making a profit each time."These problems involve calculating probabilities involving certain events, such as the failure of light bulbs, customer arrival at a store, and investment profits. Understanding these problems requires knowledge of probability theory and statistical distributions.

"Since you have asked multiple questions, we will solve the first question for you. If you want any…

Answered: 6) A certain kind of light bulb lasts 1…

6) A certain kind of light bulb lasts 1 year on average. What is the probability that a given light bulb will fail in less than a year?

Calculus For The Life Sciences

2nd Edition

ISBN:9780321964038

Author:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.

Publisher:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.

Chapter12: Probability

Section12.CR: Chapter 12 Review

Problem 15CR

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Question

For each problem:

a) Identify whether the best distribution to solve the problem is Binomial, Poisson, or Exponential.

b) Identify the correct value of all associated parameters.

c) Find the indicated probability to 4 decimal places.

### Probability Problems:

**Problem 6:**

"A certain kind of light bulb lasts 1 year on average. What is the probability that a given light bulb will fail in less than a year?"

**Problem 7:**

"Suppose that the expected number of customers at a convenience store is 5 every 20 minutes. In a given 20-minute time period, find the probability of having more than 3 customers."

**Problem 8:**

"Find the probability that an investor makes a profit on 6 of her next 12 investments, assuming independence and a 0.6 chance of making a profit each time."

These problems involve calculating probabilities involving certain events, such as the failure of light bulbs, customer arrival at a store, and investment profits. Understanding these problems requires knowledge of probability theory and statistical distributions.

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