Answer part a through d.Suppose X is normally distributed random varible with u= 15 and o=2. Find each probability. ### Finding Probabilities for a Normally Distributed Random Variable#### Problem Statement:Suppose $ x $ is a normally distributed random variable with a mean ($ \mu $) of 15 and a standard deviation ($ \sigma $) of 2. Find each of the following probabilities:a. $ P(x \geq 17.5) $b. $ P(x \leq 13.5) $c. $ P(16.58 \leq x \leq 20.22) $d. $ P(9.72 \leq x \leq 17.76) $Click [here](#) to view a table of areas under the standardized normal curve.---#### Solution:a. $ P(x \geq 17.5) $\[ P(x \geq 17.5) = \boxed{\ } \ \ (Round to three decimal places as needed.) \]---For detailed analysis and solution of each probability, use the standard normal distribution table or relevant software tools.

Answered: Suppose x is a normally distributed…

MATLAB: An Introduction with Applications

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ISBN:9781119256830

Author:Amos Gilat

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Answer part a through d.

Suppose X is normally distributed random varible with u= 15 and o=2. Find each probability.

### Finding Probabilities for a Normally Distributed Random Variable

#### Problem Statement:
Suppose $ x $ is a normally distributed random variable with a mean ($ \mu $) of 15 and a standard deviation ($ \sigma $) of 2. Find each of the following probabilities:

a. $ P(x \geq 17.5) $

b. $ P(x \leq 13.5) $

c. $ P(16.58 \leq x \leq 20.22) $

d. $ P(9.72 \leq x \leq 17.76) $

Click [here](#) to view a table of areas under the standardized normal curve.

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#### Solution:

a. $ P(x \geq 17.5) $

\[ P(x \geq 17.5) = \boxed{\ } \ \ (Round to three decimal places as needed.) \]

---

For detailed analysis and solution of each probability, use the standard normal distribution table or relevant software tools.

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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