Consider simulating the average roll of five fair 6-sided dice.Below is a histogram of the simulated average over $10000$ trials. Based on the simulation,approximate the probability that the average roll is between (and including)3 and 4.Note: This is equivalently,the probability that the sum of the five rolls is between (and including)15 and 20.
A)0.45
B)0.55
C)0.65
D)0.75
E)0.85

Question

Consider simulating the average roll of five fair 6-sided dice.Below is a histogram of the simulated average over $10000$ trials.  Based on the simulation,approximate the probability that the average roll is between (and including)3 and 4.Note: This is equivalently,the probability that the sum of the five rolls is between (and including)15 and 20.
A)0.45 
B)0.55 
C)0.65 
D)0.75 
E)0.85

Quizplus · Accepted Answer

Looking at the histogram, we can see that the majority of the averages fall between 3 and 4.5. We can estimate the probability by counting the number of trials where the average was between 3 and 4.5 and dividing it by the total number of trials (11,000 in this case).  
The number of trials where the average was between 3 and 4.5 is approximately 6,050. 
So, the estimated probability is 6,050/11,000 = 0.55. 
Therefore, the best choice is B.

Consider Simulating the Average Roll of Five Fair 6-Sided Dice 100001000010000

Consider Simulating the Average Roll of Five Fair 6-Sided Dice $10000$