Assume a member is selected at random from the population represented by the graph. Find the probability that the member selected at random is from the shaded region of the graph. Assume the variable x is normally distributed. **Problem Statement:**Assume a member is selected at random from the population represented by the graph. Find the probability that the member selected at random is from the shaded region of the graph. Assume the variable $ x $ is normally distributed.**Graph Description:**The graph displays a normal distribution curve labeled "Standardized Test Composite Scores." The mean ($\mu$) of the distribution is 20.9, and the standard deviation ($\sigma$) is 5.2.- The score range for the entire graph spans from 6 to an unspecified high value on the x-axis.- The shaded region of interest lies between scores 27 and 33.- This region represents the probability area that needs to be calculated.**Instruction for Calculation:**The objective is to determine the probability that a randomly selected member falls within the shaded area (scores between 27 and 33). The final answer should be rounded to four decimal places where needed.**Solution:**The probability that the member selected at random is from the shaded area of the graph is $\_$.(Note: The blank is indicative of the space where the final probability value should be inserted after calculation.)

Name: Assume a member is selected at random from the population represented
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Description: Assume a member is selected at random from the population represented by the graph. Find the probability that the member selected at random is from the shaded region of the graph. Assume the variable x is normally distributed. **Problem Statement:**A

Here μ = 20.9 and σ = 5.2 We Know that, Z = X-μσ then, When X= 27, Z=…

Answered: Assume a member is selected at random…

MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

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Section: Chapter Questions

Problem 1P

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Assume a member is selected at random from the population represented by the graph. Find the probability that the member selected at random is from the shaded region of the graph. Assume the variable x is normally distributed.

**Problem Statement:**

Assume a member is selected at random from the population represented by the graph. Find the probability that the member selected at random is from the shaded region of the graph. Assume the variable $ x $ is normally distributed.

**Graph Description:**

The graph displays a normal distribution curve labeled "Standardized Test Composite Scores." The mean ($\mu$) of the distribution is 20.9, and the standard deviation ($\sigma$) is 5.2.

- The score range for the entire graph spans from 6 to an unspecified high value on the x-axis.
- The shaded region of interest lies between scores 27 and 33.
- This region represents the probability area that needs to be calculated.

**Instruction for Calculation:**

The objective is to determine the probability that a randomly selected member falls within the shaded area (scores between 27 and 33). The final answer should be rounded to four decimal places where needed.

**Solution:**

The probability that the member selected at random is from the shaded area of the graph is $\_$.

(Note: The blank is indicative of the space where the final probability value should be inserted after calculation.)

Features Features Normal distribution is characterized by two parameters, mean (µ) and standard deviation (σ). When graphed, the mean represents the center of the bell curve and the graph is perfectly symmetric about the center. The mean, median, and mode are all equal for a normal distribution. The standard deviation measures the data's spread from the center. The higher the standard deviation, the more the data is spread out and the flatter the bell curve looks. Variance is another commonly used measure of the spread of the distribution and is equal to the square of the standard deviation.

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