The daily amount of coffee, in liters, dispensed by a machine located in an airport lobby is a random variable X having a continuous uniform distribution with A=7 and B = 10. Find the probability that on a given day the amount of coffee dispensed by this machine will be (a) at most 8.5 liters; (b) more than 7.5 liters but less than 8.7 liters; (c) at least 9.1 liters. (a) The probability is (Simplify your answer.) (b) The probability is (Simplify your answer.) (c) The probability is (Simplify your answer.) ..
The daily amount of coffee, in liters, dispensed by a machine located in an airport lobby is a random variable X having a continuous uniform distribution with A=7 and B = 10. Find the probability that on a given day the amount of coffee dispensed by this machine will be (a) at most 8.5 liters; (b) more than 7.5 liters but less than 8.7 liters; (c) at least 9.1 liters. (a) The probability is (Simplify your answer.) (b) The probability is (Simplify your answer.) (c) The probability is (Simplify your answer.) ..
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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![**Understanding Uniform Distribution through a Real-world Example**
In this example, we explore a real-world application involving the distribution of coffee dispensed by a machine located in an airport lobby. The amount of coffee dispensed daily by this machine is modeled as a continuous uniform random variable \( X \) with parameters \( A = 7 \) and \( B = 10 \). Our goal is to find the probability for different scenarios regarding the amount of coffee dispensed by the machine.
To facilitate this, let's break it down into different cases:
**Given:**
- Continuous uniform distribution parameters: \( A = 7 \) liters, \( B = 10 \) liters.
**Tasks:**
(a) Find the probability that the amount of coffee dispensed on a given day is at most 8.5 liters.
(b) Find the probability that the amount of coffee dispensed on a given day is more than 7.5 liters but less than 8.7 liters.
(c) Find the probability that the amount of coffee dispensed on a given day is at least 9.1 liters.
### Solutions:
1. **Case (a) - At most 8.5 liters:**
\[ \text{The probability is } \boxed{\quad}. \]
(Simplify your answer.)
2. **Case (b) - More than 7.5 liters but less than 8.7 liters:**
\[ \text{The probability is } \boxed{\quad}. \]
(Simplify your answer.)
3. **Case (c) - At least 9.1 liters:**
\[ \text{The probability is } \boxed{\quad}. \]
(Simplify your answer.)
Understanding uniform distribution helps in modeling and predicting behaviors in various practical applications. Fill in the values and simplify your answers to deepen your grasp of this concept!](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F7167d01a-fc0a-4c3f-ab49-29dc29956a80%2F411937f7-3f54-408f-9426-a3eac64bf646%2Fpa8bahl_processed.png&w=3840&q=75)
Transcribed Image Text:**Understanding Uniform Distribution through a Real-world Example**
In this example, we explore a real-world application involving the distribution of coffee dispensed by a machine located in an airport lobby. The amount of coffee dispensed daily by this machine is modeled as a continuous uniform random variable \( X \) with parameters \( A = 7 \) and \( B = 10 \). Our goal is to find the probability for different scenarios regarding the amount of coffee dispensed by the machine.
To facilitate this, let's break it down into different cases:
**Given:**
- Continuous uniform distribution parameters: \( A = 7 \) liters, \( B = 10 \) liters.
**Tasks:**
(a) Find the probability that the amount of coffee dispensed on a given day is at most 8.5 liters.
(b) Find the probability that the amount of coffee dispensed on a given day is more than 7.5 liters but less than 8.7 liters.
(c) Find the probability that the amount of coffee dispensed on a given day is at least 9.1 liters.
### Solutions:
1. **Case (a) - At most 8.5 liters:**
\[ \text{The probability is } \boxed{\quad}. \]
(Simplify your answer.)
2. **Case (b) - More than 7.5 liters but less than 8.7 liters:**
\[ \text{The probability is } \boxed{\quad}. \]
(Simplify your answer.)
3. **Case (c) - At least 9.1 liters:**
\[ \text{The probability is } \boxed{\quad}. \]
(Simplify your answer.)
Understanding uniform distribution helps in modeling and predicting behaviors in various practical applications. Fill in the values and simplify your answers to deepen your grasp of this concept!
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