SAT Writing scores are distributed in population with u = 487 and o = 115. What is the probability that a random sample of 64 test takers will have a mean SAT Writing score of 500 or higher? O.82 O.46 O.18 O.54
SAT Writing scores are distributed in population with u = 487 and o = 115. What is the probability that a random sample of 64 test takers will have a mean SAT Writing score of 500 or higher? O.82 O.46 O.18 O.54
A First Course in Probability (10th Edition)
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ISBN:9780134753119
Author:Sheldon Ross
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![**SAT Writing Scores Probability Question**
SAT Writing scores are distributed in a population with a mean (μ) of 487 and a standard deviation (σ) of 115. What is the probability that a random sample of 64 test-takers will have a mean SAT Writing score of 500 or higher?
**Answer Choices:**
- ⃝ .82
- ⃝ .46
- ⃝ .18
- ⃝ .54
This question is designed to test your understanding of the normal distribution and sampling. Given the mean (μ) and standard deviation (σ) of SAT Writing scores, and a sample size (n) of 64, you need to calculate the probability of the sample mean being 500 or higher using the properties of the normal distribution.
To solve this, you would typically use the z-score formula for a sample mean:
\[ Z = \frac{\bar{X} - \mu}{\sigma / \sqrt{n}} \]
Where:
- \(\bar{X}\) is the sample mean
- \(\mu\) is the population mean
- \(\sigma\) is the population standard deviation
- \(n\) is the sample size
Then, use the z-score to find the corresponding probability from the standard normal distribution table.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F7a520971-fd90-49dd-bfdc-9027208d76cd%2F0dfa3c9e-9b4f-4f35-93ee-db6920b28942%2F2yjgq2s_processed.png&w=3840&q=75)
Transcribed Image Text:**SAT Writing Scores Probability Question**
SAT Writing scores are distributed in a population with a mean (μ) of 487 and a standard deviation (σ) of 115. What is the probability that a random sample of 64 test-takers will have a mean SAT Writing score of 500 or higher?
**Answer Choices:**
- ⃝ .82
- ⃝ .46
- ⃝ .18
- ⃝ .54
This question is designed to test your understanding of the normal distribution and sampling. Given the mean (μ) and standard deviation (σ) of SAT Writing scores, and a sample size (n) of 64, you need to calculate the probability of the sample mean being 500 or higher using the properties of the normal distribution.
To solve this, you would typically use the z-score formula for a sample mean:
\[ Z = \frac{\bar{X} - \mu}{\sigma / \sqrt{n}} \]
Where:
- \(\bar{X}\) is the sample mean
- \(\mu\) is the population mean
- \(\sigma\) is the population standard deviation
- \(n\) is the sample size
Then, use the z-score to find the corresponding probability from the standard normal distribution table.
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