MATLAB: An Introduction with Applications
MATLAB: An Introduction with Applications
6th Edition
ISBN: 9781119256830
Author: Amos Gilat
Publisher: John Wiley & Sons Inc
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Question
Assume the random variable X is normally distributed with mean μ = 50 and standard deviation σ = 7. Find the 78th percentile. Click the icon to view a table of areas under the normal curve. The 78th percentile is [ ]. (Round to two decimal places as needed.)
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Transcribed Image Text:Assume the random variable X is normally distributed with mean μ = 50 and standard deviation σ = 7. Find the 78th percentile. Click the icon to view a table of areas under the normal curve. The 78th percentile is [ ]. (Round to two decimal places as needed.)
**Tables of Areas under the Normal Curve** *Timestamp: 10/8/23, 8:59 PM* --- ### Graph Explanation: To the left of the table is a bell-shaped curve representing a standard normal distribution. The shaded area under the curve corresponds to the probability or area for a given z-score, labeled as "z." This graph visually represents the area under the curve to the left of a specified z-score. ### Table V: Standard Normal Distribution This table is used to find the area under the standard normal curve to the left of a given z-score. The z-scores are provided in the rows, and decimal places are extended across columns labeled .00 to .09. #### Example Values: - **z = -3.4**: - Area for .00 = 0.0003 - Area for .01 = 0.0003 - Area for .02 = 0.0003 - Area for .03 = 0.0003 - Area for .04 = 0.0003 - **z = 0.0**: - Area for .00 = 0.5000 - Area for .01 = 0.5040 - Area for .02 = 0.5080 - Area for .03 = 0.5120 - Area for .04 = 0.5160 - **z = 1.0**: - Area for .00 = 0.8413 - Area for .01 = 0.8438 - Area for .02 = 0.8461 - Area for .03 = 0.8485 - Area for .04 = 0.8508 - **z = 2.5**: - Area for .00 = 0.9938 - Area for .01 = 0.9941 - Area for .02 = 0.9943 - Area for .03 = 0.9946 - Area for .04 = 0.9948 The table continues in a similar pattern, providing the cumulative area under the curve for various z-scores. This is a critical tool for statistical calculations involving the normal distribution.
expand button
Transcribed Image Text:**Tables of Areas under the Normal Curve** *Timestamp: 10/8/23, 8:59 PM* --- ### Graph Explanation: To the left of the table is a bell-shaped curve representing a standard normal distribution. The shaded area under the curve corresponds to the probability or area for a given z-score, labeled as "z." This graph visually represents the area under the curve to the left of a specified z-score. ### Table V: Standard Normal Distribution This table is used to find the area under the standard normal curve to the left of a given z-score. The z-scores are provided in the rows, and decimal places are extended across columns labeled .00 to .09. #### Example Values: - **z = -3.4**: - Area for .00 = 0.0003 - Area for .01 = 0.0003 - Area for .02 = 0.0003 - Area for .03 = 0.0003 - Area for .04 = 0.0003 - **z = 0.0**: - Area for .00 = 0.5000 - Area for .01 = 0.5040 - Area for .02 = 0.5080 - Area for .03 = 0.5120 - Area for .04 = 0.5160 - **z = 1.0**: - Area for .00 = 0.8413 - Area for .01 = 0.8438 - Area for .02 = 0.8461 - Area for .03 = 0.8485 - Area for .04 = 0.8508 - **z = 2.5**: - Area for .00 = 0.9938 - Area for .01 = 0.9941 - Area for .02 = 0.9943 - Area for .03 = 0.9946 - Area for .04 = 0.9948 The table continues in a similar pattern, providing the cumulative area under the curve for various z-scores. This is a critical tool for statistical calculations involving the normal distribution.
Expert Solution
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Step 1: Determine the given data in the question

Given that,

X tilde N left parenthesis mu equals 50 comma sigma equals 7 right parenthesis

To find the 78th percentile.


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