Question

There is a claim that 1 in every 12 widgets has a defect. Identify all of the simulations that can accurately test the claim.

A) Use a spinner with a section for 12% of the area and a section for 88% of the area.
B) Choose from a set of 12 marbles with 1 red marble, 5 blue marbles, and 6 green marbles.
C) Use two dice, with rolling two 1s as a defective widget and all other events as no defects.
D) Toss a coin 6 times, with exactly 1 head as a defective widget and all other events as no defects.
E) Use a random number generator with a minimum value of 1 and a maximum value of 12.

Answer 1

Simulations A (spinner), B (marbles), and E (random number generator) accurately test the 1 in 12 defect claim. Simulation C (dice) and D (coin toss) do not accurately reflect the probability of a defect.

Step-by-step explanation:

To test the claim that 1 in every 12 widgets has a defect, we can examine each simulation option to determine if they accurately represent a 1/12 probability of defects.

• Option A: Using a spinner with 12% designated for defects and 88% for no defects is a correct representation of the claim since 12% corresponds to 1 out of 12.
• Option B: Choosing from a set of 12 marbles with 1 red (defective) is accurate because it reflects the claim's ratio directly—1 defective marble out of 12.
• Option C: Rolling two dice and designating a double 1s roll as defect does not simulate the 1/12 probability correctly because the chance of rolling double 1s is 1/36, which is less likely than 1/12.
• Option D: Tossing a coin 6 times with 1 head indicating a defect is incorrect because this does not create a 1 in 12 probability – the outcomes are more complex and based on the binomial distribution.
• Option E: A random number generator set between 1 and 12, inclusive, will model the claim accurately since each number has an equal chance of being generated, including the number representing a defect.

Therefore, Simulations A, B, and E would accurately test the 1 in 12 defect claim.