A spinner has sections that are numbered 1 through 6. Naomi spins the spinner 12 times and records her results in the dot plot. Use the results to predict the number of times the s... A spinner has sections that are numbered 1 through 6. Naomi spins the spinner 12 times and records her results in the dot plot. Use the results to predict the number of times the spinner will land on an even number in 240 trials.

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Understand the Problem

The question describes an experiment where a spinner with sections numbered 1 through 6 is spun 12 times, and the results are recorded in a dot plot. The task is to use the results from the dot plot to predict how many times the spinner will land on an even number if it's spun 240 times.

Answer

120
Answer for screen readers

120

Steps to Solve

  1. Count the number of even results from the dot plot

The even numbers on the spinner are 2, 4, and 6. From the dot plot, we see that 0 times it landed on 2, 5 times it landed on 4, and 1 time it landed on 6. Adding these up:

$0 + 5 + 1 = 6$

  1. Calculate the probability of landing on an even number

The spinner was spun a total of 12 times. The number of times it landed on an even number was 6. Therefore, the probability of landing on an even number is:

$P(\text{even}) = \frac{\text{Number of even results}}{\text{Total number of spins}} = \frac{6}{12} = \frac{1}{2}$

  1. Predict the number of times the spinner will land on an even number in 240 trials

To predict how many times the spinner will land on an even number in 240 trials, we multiply the probability of landing on an even number by the number of trials:

$\text{Predicted number of even results} = P(\text{even}) \times \text{Number of trials} = \frac{1}{2} \times 240 = 120$

120

More Information

The experimental probability from the given 12 trials is used to predict the outcome of 240 trials.

Tips

A common mistake is misreading the dot plot or miscalculating the probability. Another mistake is forgetting to multiply the probability by the new number of trials to get the predicted number of even results. Counting the number of odd results instead of even is also a common error.

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