8 ### Normal Distribution and ProbabilityAssume the readings on thermometers are normally distributed with a mean of $0^\circ C$ and a standard deviation of $1.00^\circ C$. Find the probability that a randomly selected thermometer reads between $-1.33$ and $-0.45$ and draw a sketch of the region.#### Steps to Solve:1. Identify the mean ($\mu$) and standard deviation ($\sigma$) for the normal distribution: - Mean ($\mu$): $0^\circ C$ - Standard deviation ($\sigma$): $1.00^\circ C$ 2. Look up the corresponding values in the Z-table for the Z-scores: - Z-score for $-1.33$ - Z-score for $-0.45$#### Visual Representation:**Choose the correct graph that represents the region between $-1.33$ and $-0.45$.**- **A:** (Graph image) The shaded area is the section of the normal distribution curve between Z = $-1.33$ and Z = $-0.45$. However, shading is on the left side of $-1.33$.- **B:** (Graph image) The shaded area correctly represents the normal distribution curve between Z = $-1.33$ and Z = $-0.45$.- **C:** (Graph image) The shaded area is the section of the normal distribution curve between Z = $-1.33$ and Z = $-0.45$, but shading continues far right to other areas.**The correct graph is B:**(Graph image fully shaded between $-1.33$ and $-0.45$)#### Calculate the Probability:The probability is ________(Round to four decimal places as needed.)**Resources:**- [Page 1 of the table](#)- [Page 2 of the table](#)This example illustrates how to determine probabilities for specific ranges in a normal distribution using Z-scores and lookup tables.

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Assume the readings on thermometers are normally distributed with a mean of 0°C and a standard deviation of 1.00°C. Find the probability that a randomly selected thermometer reads between - 1.33 and - 0.45 and draw a sketch of the region. Click to view page 1 of the table. Click to view page 2 of the table. Sketch the region. Choose the correct graph below. O A. OB. Oc. -1.33 0.45 -1.33 0.45 -1.33 0.45 The probability is (Round to four decimal places as needed.)

Assume the readings on thermometers are normally distributed with a mean of 0°C and a standard deviation of 1.00°C. Find the probability that a randomly selected thermometer reads between - 1.33 and - 0.45 and draw a sketch of the region. Click to view page 1 of the table. Click to view page 2 of the table. Sketch the region. Choose the correct graph below. O A. OB. Oc. -1.33 0.45 -1.33 0.45 -1.33 0.45 The probability is (Round to four 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

### Normal Distribution and Probability

Assume the readings on thermometers are normally distributed with a mean of $0^\circ C$ and a standard deviation of $1.00^\circ C$. Find the probability that a randomly selected thermometer reads between $-1.33$ and $-0.45$ and draw a sketch of the region.

#### Steps to Solve:

1. Identify the mean ($\mu$) and standard deviation ($\sigma$) for the normal distribution:
- Mean ($\mu$): $0^\circ C$
- Standard deviation ($\sigma$): $1.00^\circ C$

2. Look up the corresponding values in the Z-table for the Z-scores:
- Z-score for $-1.33$
- Z-score for $-0.45$

#### Visual Representation:

**Choose the correct graph that represents the region between $-1.33$ and $-0.45$.**

- **A:** (Graph image) The shaded area is the section of the normal distribution curve between Z = $-1.33$ and Z = $-0.45$. However, shading is on the left side of $-1.33$.
- **B:** (Graph image) The shaded area correctly represents the normal distribution curve between Z = $-1.33$ and Z = $-0.45$.
- **C:** (Graph image) The shaded area is the section of the normal distribution curve between Z = $-1.33$ and Z = $-0.45$, but shading continues far right to other areas.

**The correct graph is B:**
(Graph image fully shaded between $-1.33$ and $-0.45$)

#### Calculate the Probability:

The probability is ________
(Round to four decimal places as needed.)

**Resources:**
- [Page 1 of the table](#)
- [Page 2 of the table](#)

This example illustrates how to determine probabilities for specific ranges in a normal distribution using Z-scores and lookup tables.

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