Assume the readings on thermometers are normally distributed with a mean of 

0degrees°C 

and a standard deviation of 

1.00degrees°C. 

Find the probability that a randomly selected thermometer reads greater than 

negative 1.79−1.79 

and draw a sketch of the region.

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Part 1

Sketch the region. Choose the correct graph below.

A.

-1.79

A graph with a bell-shaped curve, divided into 2 regions by a line from top to bottom on the left side. The region right of the line is shaded. The z-axis below the line is labeled negative 1.79.

Your answer is correct.

B.

1.79

A graph with a bell-shaped curve, divided into 2 regions by a line from top to bottom on the right side. The region right of the line is shaded. The z-axis below the line is labeled 1.79.

C.

-1.79

A graph with a bell-shaped curve, divided into 2 regions by a line from top to bottom on the left side. The region left of the line is shaded. The z-axis below the line is labeled negative 1.79.

Part 2

The probability is 

. 9633.9633.
 
​(Round to four decimal places as​ needed.)

Choose the correct graph below.The probability is(Round to four decimal places as needed.)

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To find the probability that a randomly selected thermometer reads greater than -1.79 degrees Celsius, we will use the standard normal distribution (Z-distribution).

Given:
- Mean (μ) = 0°C
- Standard deviation (σ) = 1°C
- Z score for -1.79

We need to find \( P(Z > -1.79) \).

### Step 1: Find the cumulative probability for Z = -1.79
Using the standard normal distribution table or a calculator:

\( P(Z < -1.79) \) ≈ 0.0367

### Step 2: Find the probability that Z is greater than -1.79
Since the total area under the standard normal curve is 1:

\( P(Z > -1.79) = 1 - P(Z < -1.79) \)

\( P(Z > -1.79) = 1 - 0.0367 = 0.9633 \)

So, the probability that a randomly selected thermometer reads greater than -1.79 degrees Celsius is approximately 0.9633.

### Step 3: Draw the sketch of the region

The correct graph is:

**A**. The graph with a bell-shaped curve, divided into 2 regions by a line from top to bottom on the left side. The region right of the line is shaded. The z-axis below the line is labeled -1.79.

### Summary
The probability that a randomly selected thermometer reads greater than -1.79 is 0.9633.

Do you want details or have any questions?

Here are 5 more questions you might want to ask:
1. How do you find the area under the normal curve for a given z score?
2. What is the significance of the z score in normal distribution?
3. How can you use the standard normal distribution table for different mean and standard deviation values?
4. What is the process of converting raw scores to z scores?
5. How do you interpret the results from a normal distribution table?

**Tip:** Always ensure you understand whether the table provides cumulative probabilities from the left or right to avoid confusion in finding the correct probabilities.

Calculate the probability that a randomly selected thermometer reads greater than -1.79 degrees Celsius using the standard normal distribution. Learn the step-by-step process with detailed explanations and a graphical representation.

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