Ross has a spinner that is split into eight equal sections numbered 1 through He spun the spinner 1,576 times. Which of the following would be a good estimate of the number of times the spinner landed on the number 6?
A. 268
B. 409
C. 176
D. 191
Since there are eight sections on the spinner, and each section has an equal chance of landing face-up when spun, we can estimate that the number 6 will come up approximately 1/8th of the time.
To find out how many times we can expect the spinner to land on 6 out of 1576 total spins, we can set up the following proportion:
6/8 = x/1576
Where x is the number of times we can expect the spinner to land on 6.
Simplifying the proportion:
6 * 1576 = 8 * x
9426 = x * 8
x ≈ 1178
So we can estimate that the spinner will land on the number 6 around 1178 times out of 1576 total spins.
The answer choice that is closest to this estimate is A: 268. Therefore, we can eliminate choices C and D.
Answer B is much too high and would imply that the spinner landed on 6 almost one third of the time, which is unlikely given that each section has an equal chance. Therefore, our best estimate from the answer choices is A: 268.
To determine a good estimate of the number of times the spinner landed on the number 6, we need to find the fraction of times it would be expected to land on 6 and multiply it by the total number of spins.
Since the spinner is split into eight equal sections, each number from 1 to 8 has an equal chance of being landed on. Therefore, the fraction of times it would be expected to land on 6 is 1/8.
To find the estimate, we multiply the fraction by the total number of spins: (1/8) * 1,576 = 197.
The closest option to our estimate of 197 is D. 191.