**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- ⃝ .54This 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 sizeThen, use the z-score to find the corresponding probability from the standard normal distribution table.

SAT writing scores are distributed in population with mean of 487 and standard deviation of 115.

Answered: SAT Writing scores are distributed in…

A First Course in Probability (10th Edition)

10th Edition

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Author:Sheldon Ross

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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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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