Let x = red blood cell (RBC) count in millions per cubic millimeter of whole blood. For healthy females, x has an approximately normal distribution with mean ? = 5.6 and standard deviation ? = 0.6. ### Understanding Normal Distribution in Red Blood Cell (RBC) CountRed blood cell (RBC) count in millions per cubic millimeter of whole blood can be analyzed using normal distribution. For healthy females, this distribution has a mean \( \mu \) of 5.6 and a standard deviation \( \sigma \) of 0.6.#### Standard Normal DistributionThe standard normal distribution, often denoted as \( N(0,1) \), is a normal distribution with mean \( \mu = 0 \) and standard deviation \( \sigma = 1 \). The graph provided illustrates this distribution, showing the percentage of the total area (representing probability) within specific ranges of z-values:- 68% of the area falls within 1 standard deviation (between -1 and 1).- 95% of the area falls within 2 standard deviations (between -2 and 2).- 99.7% of the area falls within 3 standard deviations (between -3 and 3).![Standard Normal Distribution](graph-image-placeholder.png)#### Conversion and InterpretationUsing the normal distribution properties, you can convert specific x-values (RBC counts) to z-scores and vice versa.(a) Convert the x interval, \( 4.5 < x \), to a z interval. (Round your answer to two decimal places.)\[ \boxed{} < z \](b) Convert the x interval, \( x < 4.2 \), to a z interval. (Round your answer to two decimal places.)\[ z < \boxed{} \](c) Convert the x interval, \( 4.0 < x < 5.5 \), to a z interval. (Round your answers to two decimal places.)\[ \boxed{} < z < \boxed{} \](d) Convert the z interval, \( z < -1.44 \), to an x interval. (Round your answer to one decimal place.)\[ x < \boxed{} \](e) Convert the z interval, \( 1.28 < z \), to an x interval. (Round your answer to one decimal place.)\[ \boxed{} < x \](f) Convert the z interval, \( -2.25 < z < -1.00 \), to an x interval. (Round your answers to one decimal place.)\[ \boxed{} < x < \boxed{} \](g) If

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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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Let x = red blood cell (RBC) count in millions per cubic millimeter of whole blood. For healthy females, x has an approximately normal distribution with mean ? = 5.6 and standard deviation ? = 0.6.

### Understanding Normal Distribution in Red Blood Cell (RBC) Count

Red blood cell (RBC) count in millions per cubic millimeter of whole blood can be analyzed using normal distribution. For healthy females, this distribution has a mean \( \mu \) of 5.6 and a standard deviation \( \sigma \) of 0.6.

#### Standard Normal Distribution

The standard normal distribution, often denoted as \( N(0,1) \), is a normal distribution with mean \( \mu = 0 \) and standard deviation \( \sigma = 1 \). The graph provided illustrates this distribution, showing the percentage of the total area (representing probability) within specific ranges of z-values:
- 68% of the area falls within 1 standard deviation (between -1 and 1).
- 95% of the area falls within 2 standard deviations (between -2 and 2).
- 99.7% of the area falls within 3 standard deviations (between -3 and 3).

![Standard Normal Distribution](graph-image-placeholder.png)

#### Conversion and Interpretation

Using the normal distribution properties, you can convert specific x-values (RBC counts) to z-scores and vice versa.

(a) Convert the x interval, \( 4.5 < x \), to a z interval. (Round your answer to two decimal places.)
\[ \boxed{} < z \]

(b) Convert the x interval, \( x < 4.2 \), to a z interval. (Round your answer to two decimal places.)
\[ z < \boxed{} \]

(c) Convert the x interval, \( 4.0 < x < 5.5 \), to a z interval. (Round your answers to two decimal places.)
\[ \boxed{} < z < \boxed{} \]

(d) Convert the z interval, \( z < -1.44 \), to an x interval. (Round your answer to one decimal place.)
\[ x < \boxed{} \]

(e) Convert the z interval, \( 1.28 < z \), to an x interval. (Round your answer to one decimal place.)
\[ \boxed{} < x \]

(f) Convert the z interval, \( -2.25 < z < -1.00 \), to an x interval. (Round your answers to one decimal place.)
\[ \boxed{} < x < \boxed{} \]

(g) If

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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