Answer:
A game would need to be at least 257.67 minutes long to qualify for the Endurance Board.
257.67 minutes = 257 minutes, 40 seconds = 4 hours, 17 minutes, 40 seconds.
Step-by-step explanation:
Games that are given special recognition on the Endurance Board are the games that last in the longest 1% of all games.
If X is the random variable that represents the time a chess game takes before it is completed.
X is said to be normally distributed with
Mean = μ = 153 minutes
Standard deviation = σ = 45 minutes
Let games that last the longest 1% of the time last for a minimum of x' minutes.
P(X > x') = 1% = 0.01
P(X ≤ x') = 1 - P(X > x') = 1 - 0.01
P(X ≤ x') = 0.99
Indicating that such games are longer than 99% of all chess games.
This is a normal distribution problem
Let the z-score for these type of longest games with a minimum duration of x' minutes be z'.
P(X ≤ x') = P(z ≤ z') = 0.99
From the normal distribution table, z' = 2.326
z-score of any value is given as the value minus the mean divided by the standard deviation.
z = (x - μ)/σ
So,
z' = (x' - μ)/σ
2.326 = (x' - 153)/45
x' = (2.326×45) + 153
x' = 104.67 + 153 = 257.67 minutes = 257 minutes, 40 seconds.
Hope this Helps!!!
