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This page shows questions in the Alg II Interpreting Categorical and Quantitative Data public release module at MSDE. Algebra 2
"Alg II Interpreting Categorical and Quantitative Data"

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This is a multiple choice question that allows you to select only one option.

Gina rolled two number cubes, each numbered from 1 to 6, and calculated the sum of the two numbers landing face up. She repeated the process 100 times, and only once did she record a sum of 2. She suspected that the cubes might not be fair.

Gina reasoned that if the cubes were fair, the probability of rolling the sum of 2 is fraction with numerator of one and denominator of 36. For 100 rolls, 100 open parentheses fraction with numerator of one and denominator of 36 close parentheses is approximately equal to 2 point 8. She thought she should have seen the sum about two or three times in 100 rolls.

Under the assumption that the cubes are fair, she conducted a simulation to determine what is a plausible number of times to observe the sum in 100 rolls. The results of 50 trials of the simulation are shown in the table.

Results of Simulation
Observations of the Sum Frequency out of 50
no times 4
one time 5
two times 10
three times 14
four times 10
five times 4
six times 2
seven times 1

Based on the results of the simulation, is there statistical evidence that Gina's number cubes are not fair?

  1. A.
    Yes. The greatest frequency in the simulation is 14, indicating that the sum should have been observed three times. The number cubes are not fair.
  2. B.
    Yes. Observing the sum only one time out of 100 is equal to the probability of 0.01. Such a small probability indicates that the number cubes are not fair.
  3. C.
    No. Observing the sum once or never occurred in 18% of the trials, indicating that the observation is plausible. There is no evidence that the number cubes are not fair.
  4. D.
    No. The sum was observed from a minimum of no times to a maximum of seven times in the simulation. Observing the sum one time falls within the interval of one to seven. The number cubes are fair.

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