Final answer:
The probability of a major league baseball game duration being fewer than 175 minutes, given the game durations are normally distributed with a mean of 150 minutes and a standard deviation of 30 minutes, is approximately 79.67%.
Step-by-step explanation:
To find the probability of a major league baseball game duration being fewer than 175 minutes when the durations are normally distributed with a mean of 150 minutes and a standard deviation of 30 minutes, we use the Z-score formula:
Z = (X - μ) / σ
Where:
- X is the duration of the game (175 minutes in this case)
- μ is the mean (150 minutes)
- σ is the standard deviation (30 minutes)
Substitute the values into the formula:
Z = (175 - 150) / 30
Z = 25 / 30
Z = 0.83
Now use a Z-table or standard normal distribution table to find the probability corresponding to the Z-score. The probability for Z = 0.83 is approximately 0.7967 or 79.67%. Therefore, there is a 79.67% chance that a game will last fewer than 175 minutes.