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 DistributionThis 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 = 0.9948The 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.

Given that,To find the 78th percentile.

Answered: The 78th percentile is. (Round to two…

Math

Statistics

The 78th percentile is. (Round to two decimal places as needed.)

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

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.

Expert Solution

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 78^th percentile.

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