A First Course in Probability (10th Edition)
A First Course in Probability (10th Edition)
10th Edition
ISBN: 9780134753119
Author: Sheldon Ross
Publisher: PEARSON
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**Problem Statement:** Randomly sample 256 items from a population where individuals have a normal distribution with a mean of 120 and a standard deviation of 160. Find the following probability rounded to 4 decimal places. **Graph/Diagram Explanation:** The diagram is a normal distribution curve representing the sampling distribution of the sample mean. It has a symmetric bell shape centered at the population mean of 120. The x-axis ranges from 80 to 160 with increments of 10. Below the x-axis, the corresponding z-scores are marked: - z = -4 at x = 80 - z = -2 at x = 100 - z = 0 at x = 120 (mean) - z = 2 at x = 140 - z = 4 at x = 160 The shaded area under the curve represents the probability of the sample mean falling between the given range. **Probability Expression:** \[ P(110.5 < \bar{x} < 143.2) = \] (Use this space to calculate or provide the probability value using statistical methods or tools.)
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Transcribed Image Text:**Problem Statement:** Randomly sample 256 items from a population where individuals have a normal distribution with a mean of 120 and a standard deviation of 160. Find the following probability rounded to 4 decimal places. **Graph/Diagram Explanation:** The diagram is a normal distribution curve representing the sampling distribution of the sample mean. It has a symmetric bell shape centered at the population mean of 120. The x-axis ranges from 80 to 160 with increments of 10. Below the x-axis, the corresponding z-scores are marked: - z = -4 at x = 80 - z = -2 at x = 100 - z = 0 at x = 120 (mean) - z = 2 at x = 140 - z = 4 at x = 160 The shaded area under the curve represents the probability of the sample mean falling between the given range. **Probability Expression:** \[ P(110.5 < \bar{x} < 143.2) = \] (Use this space to calculate or provide the probability value using statistical methods or tools.)
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