A particular fruit's weights are normally distributed, with a mean of 388 grams and a standard deviation of 22 grams. If you pick one fruit at random, what is the probability that it will weigh between 341 grams and 428 grams. (Give answer to 4 decimal places.)
A particular fruit's weights are normally distributed, with a mean of 388 grams and a standard deviation of 22 grams. If you pick one fruit at random, what is the probability that it will weigh between 341 grams and 428 grams. (Give answer to 4 decimal places.)
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: Probability of Picking a Fruit Within a Specified Weight Range**
A particular fruit's weights are normally distributed, with a mean of 388 grams and a standard deviation of 22 grams.
If you pick one fruit at random, what is the probability that it will weigh between 341 grams and 428 grams? (Give answer to 4 decimal places.)
*Answer Box:* [ ]
**Explanation:**
To solve this problem, you will need to use the properties of the normal distribution. This involves calculating the Z-scores for the weight limits, then referring to a standard normal distribution table or using a calculator to find the probabilities corresponding to these Z-scores.
1. **Calculate the Z-scores:**
- For 341 grams:
\[
Z = \frac{341 - 388}{22}
\]
- For 428 grams:
\[
Z = \frac{428 - 388}{22}
\]
2. **Find the probabilities:**
- Use the Z-scores to find the probabilities from a standard normal distribution table or calculator.
3. **Determine the probability of the weight being between 341 grams and 428 grams:**
- Subtract the smaller probability from the larger probability to find the difference.
This process will yield the probability that a randomly selected fruit weighs between 341 grams and 428 grams.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fd3906bba-d731-4d3e-8323-fa6146946cae%2Fa82b1f2d-b1dd-4fff-b5d3-ed899524650b%2Fn9kvzoe_processed.png&w=3840&q=75)
Transcribed Image Text:**Problem: Probability of Picking a Fruit Within a Specified Weight Range**
A particular fruit's weights are normally distributed, with a mean of 388 grams and a standard deviation of 22 grams.
If you pick one fruit at random, what is the probability that it will weigh between 341 grams and 428 grams? (Give answer to 4 decimal places.)
*Answer Box:* [ ]
**Explanation:**
To solve this problem, you will need to use the properties of the normal distribution. This involves calculating the Z-scores for the weight limits, then referring to a standard normal distribution table or using a calculator to find the probabilities corresponding to these Z-scores.
1. **Calculate the Z-scores:**
- For 341 grams:
\[
Z = \frac{341 - 388}{22}
\]
- For 428 grams:
\[
Z = \frac{428 - 388}{22}
\]
2. **Find the probabilities:**
- Use the Z-scores to find the probabilities from a standard normal distribution table or calculator.
3. **Determine the probability of the weight being between 341 grams and 428 grams:**
- Subtract the smaller probability from the larger probability to find the difference.
This process will yield the probability that a randomly selected fruit weighs between 341 grams and 428 grams.
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