To find the probability $P(Z < -0.094)$, we need to use the standard normal distribution.

Given:

• The thermometer readings are normally distributed with a mean $\mu = 0$ and a standard deviation $\sigma = 1$.
• We are looking for $P(Z < -0.094)$.

Since $Z$ represents the standard normal variable, we can directly use the z-score value of $-0.094$ to look up the cumulative probability in the standard normal distribution table or use a calculator.

1. Using the standard normal distribution table or a calculator: For $Z = -0.094$:
   • The cumulative probability $P(Z < -0.094) \approx 0.463$.

Therefore: $P(Z < -0.094) \approx 0.463$

This means there is approximately a 46.3% chance of obtaining a reading less than $-0.094^\circ C$.

Would you like more details on how to interpret this probability?

Here are 5 related questions that could deepen your understanding:

1. How would the probability change if the reading threshold was different, say $-0.5$ or $0.1$?
2. What is the probability of obtaining a reading between two values, for example, between $-0.1$ and $0.2$?
3. How would this problem change if the standard deviation was 0.5 instead of 1.0?
4. What is the probability of obtaining a reading greater than $-0.094$?
5. Can you explain why the normal distribution is appropriate for this type of problem?

Tip: When interpreting probabilities in a standard normal distribution, values close to 0.5 mean the value is near the mean, while probabilities closer to 0 or 1 indicate values far from the mean in the respective directions.