The amount of coffee in a can has a mean of 350g. The standard deviation is 5g. Use the normal distribution curve to find the probability the coffee can will have BETWEEN 340 and 350 grams of coffee in it.
The amount of coffee in a can has a mean of 350g. The standard deviation is 5g. Use the normal distribution curve to find the probability the coffee can will have BETWEEN 340 and 350 grams of coffee in it.
A First Course in Probability (10th Edition)
10th Edition
ISBN:9780134753119
Author:Sheldon Ross
Publisher:Sheldon Ross
Chapter1: Combinatorial Analysis
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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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![**Probability Distribution of Coffee Amount in Cans**
The amount of coffee in a can has a mean of 350g with a standard deviation of 5g. Use the normal distribution curve to find the probability that a coffee can will contain between 340g and 350g of coffee.
**Normal Distribution Curve Explanation:**
This graph represents a normal distribution of the amount of coffee in a can. The x-axis shows the range of coffee weights, while the y-axis represents the probability.
- **Mean (μ):** 350g
- **Standard Deviation (σ):** 5g
The area under the curve indicates the probabilities corresponding to different ranges of coffee amounts. The values written above the bars represent the probabilities for those particular segments.
**Segments Represented on the Graph:**
- **335g to 340g:** Probability = 0.0015
- **340g to 345g:** Probability = 0.0235
- **345g to 350g:** Probability = 0.135
- **350g to 355g:** Probability = 0.34
- **355g to 360g:** Probability = 0.34
- **360g to 365g:** Probability = 0.135
- **365g and beyond:** Probability = 0.0015
**Finding the Probability Between 340g and 350g:**
To find the probability that a coffee can will have between 340g and 350g of coffee, we need to sum the probabilities of the segments that fall within this range:
- **340g to 345g:** 0.0235
- **345g to 350g:** 0.135
**Total Probability:**
\[
0.0235 + 0.135 = 0.1585
\]
**Answer Choices:**
- 0.475
- 0.68
- 0.0235
- 0.815
The correct probability that the coffee can will have between 340g and 350g is **0.1585**, though none of the provided options are correct.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F867dc987-59d9-49c4-a55f-a6e769b19375%2Fa28aef8a-04a5-40a1-be1b-92dd77fb746b%2F3prbeho_processed.jpeg&w=3840&q=75)
Transcribed Image Text:**Probability Distribution of Coffee Amount in Cans**
The amount of coffee in a can has a mean of 350g with a standard deviation of 5g. Use the normal distribution curve to find the probability that a coffee can will contain between 340g and 350g of coffee.
**Normal Distribution Curve Explanation:**
This graph represents a normal distribution of the amount of coffee in a can. The x-axis shows the range of coffee weights, while the y-axis represents the probability.
- **Mean (μ):** 350g
- **Standard Deviation (σ):** 5g
The area under the curve indicates the probabilities corresponding to different ranges of coffee amounts. The values written above the bars represent the probabilities for those particular segments.
**Segments Represented on the Graph:**
- **335g to 340g:** Probability = 0.0015
- **340g to 345g:** Probability = 0.0235
- **345g to 350g:** Probability = 0.135
- **350g to 355g:** Probability = 0.34
- **355g to 360g:** Probability = 0.34
- **360g to 365g:** Probability = 0.135
- **365g and beyond:** Probability = 0.0015
**Finding the Probability Between 340g and 350g:**
To find the probability that a coffee can will have between 340g and 350g of coffee, we need to sum the probabilities of the segments that fall within this range:
- **340g to 345g:** 0.0235
- **345g to 350g:** 0.135
**Total Probability:**
\[
0.0235 + 0.135 = 0.1585
\]
**Answer Choices:**
- 0.475
- 0.68
- 0.0235
- 0.815
The correct probability that the coffee can will have between 340g and 350g is **0.1585**, though none of the provided options are correct.
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