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What percentage of the area under the normal curve lies to the right of μ+20? O 2.50% 2.10% O 16.00% 0.50% 0.15%

What percentage of the area under the normal curve lies to the right of μ+20? O 2.50% 2.10% O 16.00% 0.50% 0.15%

MATLAB: An Introduction with Applications
MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
Section: Chapter Questions
Problem 1P
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**Question:** What percentage of the area under the normal curve lies to the right of \( \mu + 2\sigma \)? **Options:** - ☐ 2.50% - ☐ 2.10% - ☐ 16.00% - ☐ 0.50% - ☐ 0.15% --- **Explanation:** In the context of a normal distribution, \( \mu \) represents the mean, and \( \sigma \) represents the standard deviation. The question asks for the percentage of the area under the normal distribution curve that lies to the right of \( \mu + 2\sigma \). **Background:** The values mentioned in the options likely refer to known probabilities associated with the standard normal distribution (i.e., a normal distribution with a mean of 0 and a standard deviation of 1). For a standard normal distribution: - Approximately 95.4% of the data falls within \( \mu \pm 2\sigma \). - This implies that the remaining 4.6% of the data falls outside this range. - Since the normal distribution is symmetric, half of this (2.3%) will lie to the right of \( \mu + 2\sigma \). However, one must consider that standard normal distribution probabilities are often memorized from standard tables or calculated via software for exact values. It's clear the closest value in the options to 2.3% is 2.10%. **Answer:** The percentage of the area under the normal curve that lies to the right of \( \mu + 2\sigma \) is approximately 2.10%. Therefore, the correct answer is: ☐ 2.10%
Transcribed Image Text:**Question:** What percentage of the area under the normal curve lies to the right of \( \mu + 2\sigma \)? **Options:** - ☐ 2.50% - ☐ 2.10% - ☐ 16.00% - ☐ 0.50% - ☐ 0.15% --- **Explanation:** In the context of a normal distribution, \( \mu \) represents the mean, and \( \sigma \) represents the standard deviation. The question asks for the percentage of the area under the normal distribution curve that lies to the right of \( \mu + 2\sigma \). **Background:** The values mentioned in the options likely refer to known probabilities associated with the standard normal distribution (i.e., a normal distribution with a mean of 0 and a standard deviation of 1). For a standard normal distribution: - Approximately 95.4% of the data falls within \( \mu \pm 2\sigma \). - This implies that the remaining 4.6% of the data falls outside this range. - Since the normal distribution is symmetric, half of this (2.3%) will lie to the right of \( \mu + 2\sigma \). However, one must consider that standard normal distribution probabilities are often memorized from standard tables or calculated via software for exact values. It's clear the closest value in the options to 2.3% is 2.10%. **Answer:** The percentage of the area under the normal curve that lies to the right of \( \mu + 2\sigma \) is approximately 2.10%. Therefore, the correct answer is: ☐ 2.10%
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