What is the explanation of this problem? ### Educational Transcription and Explanation:#### Problem Statement:Many students like to eat microwave popcorn as they study for the ACT. Microwave popcorn producers assume that the time it takes for a kernel to pop is distributed normally with a mean of 120 seconds and a standard deviation of 13 for a standard microwave oven. If you're a devoted popcorn studier, you don’t want a lot of un-popped kernels, but you know that if you leave the bag in long enough to be sure that all the kernels are popped, some of the popcorn will burn. How much time would you recommend for microwaving the popcorn? Use a normal distribution curve and the features of a normal distribution to explain your answer.#### Student's Solution:The time recommended for microwaving the popcorn will be 159 seconds, which corresponds to the 97.5% percentile.#### Graph/Diagram Explanation:- **Normal Distribution Curve:** - The bell curve is divided into different segments representing standard deviations from the mean. - **Mean (120 seconds):** Located at the center of the curve. - **Standard Deviations:** - One standard deviation (±13) from the mean includes about 68% of the data (between 107 and 133 seconds). - Two standard deviations cover about 95% (between 94 and 146 seconds). - Three standard deviations encompass about 99.7% (up to 159 seconds).- **Shaded Areas:** - Yellow and green areas represent different percentages of data falling within each standard deviation. - The numbers at the bottom (81, 94, 107, 120, 133, 146, 159) represent seconds, aligning with each standard deviation.The solution indicates that setting the microwave time to 159 seconds would ensure that 97.5% of kernels are popped, minimizing un-popped kernels while reducing the risk of burning the popcorn.#### Licensing:This problem is from the Mathematics Vision Project and is licensed under the Creative Commons Attribution CC BY 4.0. More information can be found at [mathematicsvisionproject.org](http://mathematicsvisionproject.org).---

Answered: Image /qna-images/answer/3fb356d3-bb1a-4d4e-9e5c-3a21dd468a28.jpg

5. Many students like to eat microwave popcorn as they study for the ACT. Microwave popcorm producers assume that the time it takes for a kernel to pop is distributed normally with a mean of 120 seconds and a standard deviation of 13 for a standard microwave oven. If you're a devoted popcorn studier, you don't want a lot of un-popped kernels, but you know that if you leave the bag In Tong enough to be sure that all the kernels are popped, some of the popcorn will burn. How much time would you recommend for microwaving the popcorn? Use a normal distribution curve and the features of a normal distribution to explain your answer.

5. Many students like to eat microwave popcorn as they study for the ACT. Microwave popcorm producers assume that the time it takes for a kernel to pop is distributed normally with a mean of 120 seconds and a standard deviation of 13 for a standard microwave oven. If you're a devoted popcorn studier, you don't want a lot of un-popped kernels, but you know that if you leave the bag In Tong enough to be sure that all the kernels are popped, some of the popcorn will burn. How much time would you recommend for microwaving the popcorn? Use a normal distribution curve and the features of a normal distribution to explain your answer.

Algebra and Trigonometry (6th Edition)

6th Edition

ISBN:9780134463216

Author:Robert F. Blitzer

Publisher:Robert F. Blitzer

ChapterP: Prerequisites: Fundamental Concepts Of Algebra

Section: Chapter Questions

Problem 1MCCP: In Exercises 1-25, simplify the given expression or perform the indicated operation (and simplify,...

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Question

What is the explanation of this problem?

### Educational Transcription and Explanation:

#### Problem Statement:
Many students like to eat microwave popcorn as they study for the ACT. Microwave popcorn producers assume that the time it takes for a kernel to pop is distributed normally with a mean of 120 seconds and a standard deviation of 13 for a standard microwave oven. If you're a devoted popcorn studier, you don’t want a lot of un-popped kernels, but you know that if you leave the bag in long enough to be sure that all the kernels are popped, some of the popcorn will burn. How much time would you recommend for microwaving the popcorn? Use a normal distribution curve and the features of a normal distribution to explain your answer.

#### Student's Solution:
The time recommended for microwaving the popcorn will be 159 seconds, which corresponds to the 97.5% percentile.

#### Graph/Diagram Explanation:
- **Normal Distribution Curve:**
- The bell curve is divided into different segments representing standard deviations from the mean.
- **Mean (120 seconds):** Located at the center of the curve.
- **Standard Deviations:**
- One standard deviation (±13) from the mean includes about 68% of the data (between 107 and 133 seconds).
- Two standard deviations cover about 95% (between 94 and 146 seconds).
- Three standard deviations encompass about 99.7% (up to 159 seconds).

- **Shaded Areas:**
- Yellow and green areas represent different percentages of data falling within each standard deviation.
- The numbers at the bottom (81, 94, 107, 120, 133, 146, 159) represent seconds, aligning with each standard deviation.

The solution indicates that setting the microwave time to 159 seconds would ensure that 97.5% of kernels are popped, minimizing un-popped kernels while reducing the risk of burning the popcorn.

#### Licensing:
This problem is from the Mathematics Vision Project and is licensed under the Creative Commons Attribution CC BY 4.0. More information can be found at [mathematicsvisionproject.org](http://mathematicsvisionproject.org).

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