To find the probability of obtaining a thermometer reading between $-2.443^\circ C$ and $-0.119^\circ C$, given that the readings are normally distributed with a mean $\mu = 0^\circ C$ and a standard deviation $\sigma = 1^\circ C$, we can use the standard normal distribution (z-distribution).

Steps:

1. Convert the values to z-scores: The z-score for a value $x$ in a normal distribution is calculated using the formula: $z = \frac{x - \mu}{\sigma}$

   • For $x_1 = -2.443^\circ C$: $z_1 = \frac{-2.443 - 0}{1} = -2.443$
   • For $x_2 = -0.119^\circ C$: $z_2 = \frac{-0.119 - 0}{1} = -0.119$

2. Find the cumulative probabilities for each z-score: Use standard normal distribution tables or a calculator to find the cumulative probabilities for each z-score:

   • $P(z_1 = -2.443)$
   • $P(z_2 = -0.119)$

3. Subtract the cumulative probabilities: The probability of obtaining a reading between $-2.443^\circ C$ and $-0.119^\circ C$ is: $P(-2.443 < z < -0.119) = P(z_2) - P(z_1)$

Let's compute the exact values.

I will calculate the cumulative probabilities for both z-scores.The probability of obtaining a thermometer reading between $-2.443^\circ C$ and $-0.119^\circ C$ is approximately $0.445$, or 44.5%.

Would you like a more detailed explanation or have any further questions?

Here are 5 related questions you might explore:

1. What is the probability of a reading being below $-0.119^\circ C$?
2. How do you find probabilities outside of a given range, such as above $1^\circ C$?
3. How does the standard deviation affect the shape of the normal distribution?
4. What is the probability of obtaining a reading above $1^\circ C$?
5. How can z-scores be used to compare different datasets?

Tip: When working with normal distributions, always convert raw scores into z-scores to standardize them for easy probability lookup.