Most coffee drinkers take a little time each day for their favorite beverage, and many take more than one coffee break every day. The table below, adapted from a certain newspaper, shows the probability distribution for x, the number of coffee breaks taken per day by coffee drinkers.
Most coffee drinkers take a little time each day for their favorite beverage, and many take more than one coffee break every day. The table below, adapted from a certain newspaper, shows the probability distribution for x, the number of coffee breaks taken per day by coffee drinkers.
MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
Section: Chapter Questions
Problem 1P
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This question has part a, b, c, and d.
![**Text Transcription:**
Most coffee drinkers take a little time each day for their favorite beverage, and many take more than one coffee break every day. The table below, adapted from a certain newspaper, shows the probability distribution for x, the number of coffee breaks taken per day by coffee drinkers.
| x | 0 | 1 | 2 | 3 | 4 | 5 |
|-------|------|------|------|------|------|------|
| p(x) | 0.13 | 0.18 | 0.38 | 0.27 | 0.03 | 0.01 |
**(a)** What is the probability that a randomly selected coffee drinker would take no coffee breaks during the day?
[ ]
**(b)** What is the probability that a randomly selected coffee drinker would take more than **three** coffee breaks during the day?
[ ]
**(c)** Calculate the mean and standard deviation for the random variable x. (Round your standard deviation to three decimal places.)
Mean: [_____] coffee breaks
Standard Deviation: [_____] coffee breaks
**(d)** Find the probability that x falls into the interval \( \mu \pm 2\sigma \).
[ ]
**Explanation of Table:**
- **x** represents the number of coffee breaks taken per day.
- **p(x)** represents the probability of each corresponding number of coffee breaks.
The table provides a clear distribution of probabilities for taking 0 to 5 coffee breaks, where p(x) values sum up to 1, representing all possible outcomes.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F3fdf87a1-6c5c-465d-8ddf-eaf69800c0eb%2F25465e31-c528-4170-9873-4252ccbe848c%2Fp9z2ulj_processed.png&w=3840&q=75)
Transcribed Image Text:**Text Transcription:**
Most coffee drinkers take a little time each day for their favorite beverage, and many take more than one coffee break every day. The table below, adapted from a certain newspaper, shows the probability distribution for x, the number of coffee breaks taken per day by coffee drinkers.
| x | 0 | 1 | 2 | 3 | 4 | 5 |
|-------|------|------|------|------|------|------|
| p(x) | 0.13 | 0.18 | 0.38 | 0.27 | 0.03 | 0.01 |
**(a)** What is the probability that a randomly selected coffee drinker would take no coffee breaks during the day?
[ ]
**(b)** What is the probability that a randomly selected coffee drinker would take more than **three** coffee breaks during the day?
[ ]
**(c)** Calculate the mean and standard deviation for the random variable x. (Round your standard deviation to three decimal places.)
Mean: [_____] coffee breaks
Standard Deviation: [_____] coffee breaks
**(d)** Find the probability that x falls into the interval \( \mu \pm 2\sigma \).
[ ]
**Explanation of Table:**
- **x** represents the number of coffee breaks taken per day.
- **p(x)** represents the probability of each corresponding number of coffee breaks.
The table provides a clear distribution of probabilities for taking 0 to 5 coffee breaks, where p(x) values sum up to 1, representing all possible outcomes.
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