A bag containing 10,000 beads of assorted colors is purchased from a craft store. To estimate the percent of red

Question

A bag containing 10,000 beads of assorted colors is purchased from a craft store. To estimate the percent of red beads in the bag, a sample of beads is selected at random. The percent of red beads in the bag was estimated to be 15%, with an associated margin of error of 2%. If r is the actual number of red beads in the bag, which of the following is most plausible?

A.

$r is greater than 1,700$

B.

$1,300 is less than r, which is less than 1,700$

C.

$200 is less than r, which is less than 1,500$

D.

$r is less than 1,300$

Accepted Answer

Choice B is correct. It was estimated that 15% of the beads in the bag are red. Since the bag contains 10,000 beads, it follows that there are an estimated red beads. It&rsquo;s given that the margin of error is 2%, or beads. If the estimate is too high, there could plausibly be red beads. If the estimate is too low, there could plausibly be red beads. Therefore, the most plausible statement of the actual number of red beads in the bag is . Choices A and D are incorrect and may result from misinterpreting the margin of error. It&rsquo;s unlikely that more than 1,700 beads or fewer than 1,300 beads in the bag are red. Choice C is incorrect because 200 is the margin of error for the number of red beads, not the lower bound of the range of red beads.

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