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. 80 z = -4 90 100 z = -2 110 120 P (110.5 < < 143.2) z = 0 130 140 z = 2 150 160 z = 4
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. 80 z = -4 90 100 z = -2 110 120 P (110.5 < < 143.2) z = 0 130 140 z = 2 150 160 z = 4
A First Course in Probability (10th Edition)
10th Edition
ISBN:9780134753119
Author:Sheldon Ross
Publisher:Sheldon Ross
Chapter1: Combinatorial Analysis
Section: Chapter Questions
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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![**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.)](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Ff821f9aa-4788-41c9-90a4-53f493bbfa90%2F1bce9a13-9e5b-4373-a82c-e9a0953fb141%2Fhj75azk_processed.png&w=3840&q=75)
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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