Major league baseball game durations are normally distributed with a mean of 190 minutes and a standard deviation of 35 minutes.

**What is the probability of a game duration of between 210 and 220 minutes?**

Please specify your answer in decimal terms and round your answer to the nearest hundredth (e.g., enter 12 percent as 0.12).

To find the probability of a Major League Baseball game lasting between 210 and 220 minutes, we can use the properties of the normal distribution. Here's the process:

1. **Convert the values to z-scores:**
   The formula for converting a raw score \( x \) to a z-score is:
   \[
   z = \frac{x - \mu}{\sigma}
   \]
   where:
   - \( \mu = 190 \) (mean game duration)
   - \( \sigma = 35 \) (standard deviation)

   For 210 minutes:
   \[
   z_1 = \frac{210 - 190}{35} = \frac{20}{35} \approx 0.57
   \]

   For 220 minutes:
   \[
   z_2 = \frac{220 - 190}{35} = \frac{30}{35} \approx 0.86
   \]

2. **Find the probabilities corresponding to these z-scores:**
   Using standard normal distribution tables or a calculator:

   - The probability for \( z_1 = 0.57 \) is approximately 0.7157.
   - The probability for \( z_2 = 0.86 \) is approximately 0.8051.

3. **Calculate the probability between 210 and 220 minutes:**
   The probability is the difference between the two probabilities:
   \[
   P(210 \leq X \leq 220) = P(z_2) - P(z_1) = 0.8051 - 0.7157 = 0.0894
   \]

So, the probability of a game lasting between 210 and 220 minutes is approximately **0.09**.

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Would you like further clarification, or have any questions?

Here are 5 related questions you might consider:

1. What is the probability of a game lasting more than 220 minutes?
2. How would the probability change if the mean game duration increased to 200 minutes?
3. What is the z-score for a game that lasts exactly 190 minutes?
4. How would you calculate the probability of a game lasting less than 210 minutes?
5. What is the area under the normal distribution curve for a game lasting exactly 190 minutes?

**Tip**: Always double-check your z-scores using a standard normal distribution table or calculator for precision.

What is the probability of a game duration of between 210 and 220 minutes?

Learn how to calculate the probability of a Major League Baseball game lasting between 210 and 220 minutes using normal distribution. This problem involves understanding Z-scores and applying the empirical rule. Suitable for students in Grades 10-12.

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