To find the probability of obtaining a reading between 0.907°C and 2.994°C, we will use the properties of the normal distribution.

The readings follow a normal distribution with:

• Mean ($\mu$) = 0°C
• Standard deviation ($\sigma$) = 1°C

The probability of obtaining a reading between 0.907°C and 2.994°C is equivalent to finding the area under the normal curve between these two values.

Step 1: Convert the temperatures to z-scores.

The formula for the z-score is:

$z = \frac{x - \mu}{\sigma}$

• For $x = 0.907^\circ C$:

$z_1 = \frac{0.907 - 0}{1} = 0.907$

• For $x = 2.994^\circ C$:

$z_2 = \frac{2.994 - 0}{1} = 2.994$

Step 2: Find the probabilities corresponding to these z-scores.

We can use a standard normal table or a calculator to find the probabilities for these z-scores.

• The probability corresponding to $z_1 = 0.907$ is approximately 0.8176.
• The probability corresponding to $z_2 = 2.994$ is approximately 0.9986.

Step 3: Calculate the probability between the two z-scores.

The probability of obtaining a reading between 0.907°C and 2.994°C is the difference between the two probabilities:

$P(0.907 < X < 2.994) = P(z_2) - P(z_1) = 0.9986 - 0.8176 = 0.1810$

Final Answer:

The probability of obtaining a reading between 0.907°C and 2.994°C is 0.1810 or 18.10%.

Would you like more details or have any questions?

Here are 5 related questions:

1. How do you find probabilities for values below a certain z-score?
2. What is the probability of obtaining a reading less than 0°C in this scenario?
3. How do we calculate probabilities for non-standard normal distributions?
4. How does changing the mean and standard deviation affect the probability?
5. What is the probability of obtaining a reading above 3°C?

Tip: The total area under a normal distribution curve is always 1, representing a 100% probability for all possible outcomes.