Suppose the length of voicemails (in seconds) is normally distributed with a mean of 40 seconds and standard deviation of 10 seconds. Find the probability that a given voicemail is between 10 and 30 seconds. 10 20 30 *99.7% -95% -68%- 40 50 60 70 P = [? ]%
Suppose the length of voicemails (in seconds) is normally distributed with a mean of 40 seconds and standard deviation of 10 seconds. Find the probability that a given voicemail is between 10 and 30 seconds. 10 20 30 *99.7% -95% -68%- 40 50 60 70 P = [? ]%
A First Course in Probability (10th Edition)
10th Edition
ISBN:9780134753119
Author:Sheldon Ross
Publisher:Sheldon Ross
Chapter1: Combinatorial Analysis
Section: Chapter Questions
Problem 1.1P: a. How many different 7-place license plates are possible if the first 2 places are for letters and...
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![**Title: Understanding Normal Distribution of Voicemail Lengths**
**Introduction:**
Explore the concept of normal distribution using the example of voicemail lengths.
**Problem Statement:**
Suppose the length of voicemails (in seconds) is normally distributed with a mean of 40 seconds and a standard deviation of 10 seconds. Determine the probability that a given voicemail is between 10 and 30 seconds.
**Graph Explanation:**
A bell-shaped curve represents the normal distribution of voicemail lengths.
- **Mean:** The center of the curve is at 40 seconds.
- **Standard Deviation:** The curve's spread is defined by a standard deviation of 10 seconds.
**Probability Intervals Marked on the Graph:**
- **68%:** Represents one standard deviation from the mean (30 to 50 seconds).
- **95%:** Covers two standard deviations from the mean (20 to 60 seconds).
- **99.7%:** Encompasses three standard deviations from the mean (10 to 70 seconds).
**Question:**
Calculate the probability (P) that a voicemail is between 10 and 30 seconds.
**Conclusion Placeholder:**
\[ P = \text{[?]} \% \]
This concludes the exploration of voicemail lengths and their probabilistic distribution.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F307a1d23-efde-4565-8478-e4db551b7b2c%2F19fb52a6-c961-4cbc-a4d3-9ec8c126047f%2F1t8gnsa_processed.png&w=3840&q=75)
Transcribed Image Text:**Title: Understanding Normal Distribution of Voicemail Lengths**
**Introduction:**
Explore the concept of normal distribution using the example of voicemail lengths.
**Problem Statement:**
Suppose the length of voicemails (in seconds) is normally distributed with a mean of 40 seconds and a standard deviation of 10 seconds. Determine the probability that a given voicemail is between 10 and 30 seconds.
**Graph Explanation:**
A bell-shaped curve represents the normal distribution of voicemail lengths.
- **Mean:** The center of the curve is at 40 seconds.
- **Standard Deviation:** The curve's spread is defined by a standard deviation of 10 seconds.
**Probability Intervals Marked on the Graph:**
- **68%:** Represents one standard deviation from the mean (30 to 50 seconds).
- **95%:** Covers two standard deviations from the mean (20 to 60 seconds).
- **99.7%:** Encompasses three standard deviations from the mean (10 to 70 seconds).
**Question:**
Calculate the probability (P) that a voicemail is between 10 and 30 seconds.
**Conclusion Placeholder:**
\[ P = \text{[?]} \% \]
This concludes the exploration of voicemail lengths and their probabilistic distribution.
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