Mariah is studying the life cycle of the monarch butterfly. She must choose one stage in the cycle to present in science class: egg, caterpillar, chrysalis, or adult. She plans to make her choice randomly using a custom spinner divided into four sections. First, however, she spins the spinner 50 times to see the frequencies it generates.
| Stage | Times Landed On |
| ----------- | --------------- |
| egg | 10 |
| caterpillar | 12 |
| chrysalis | 15 |
| adult | 13 |
The relative frequency of landing on egg is $\square$.
The relative frequency of landing on caterpillar is $\square$.
The relative frequency of landing on chrysalis is $\square$.
The relative frequency of landing on adult is $\square$.
All the outcomes $\square$ be considered equally likely.
Answer (2)
0.2 ; 0.24 ; 0.3 ; 0.26 ; c ann o t
Explanation
Analyze the problem and data Mariah is conducting an experiment to determine the likelihood of a spinner landing on different stages of a monarch butterfly's life cycle. She spins the spinner 50 times and records the number of times it lands on each stage: egg, caterpillar, chrysalis, and adult. We need to calculate the relative frequency for each stage and determine if the outcomes are equally likely.
Calculate relative frequencies To find the relative frequency of each stage, we divide the number of times the spinner landed on that stage by the total number of spins (50).
Egg relative frequency The relative frequency of landing on egg is 50 10 = 0.2 .
Caterpillar relative frequency The relative frequency of landing on caterpillar is 50 12 = 0.24 .
Chrysalis relative frequency The relative frequency of landing on chrysalis is 50 15 = 0.3 .
Adult relative frequency The relative frequency of landing on adult is 50 13 = 0.26 .
Determine if outcomes are equally likely Since the relative frequencies (0.2, 0.24, 0.3, and 0.26) are not all equal, the outcomes are not equally likely.
State the final answer The relative frequency of landing on egg is 0.2 . The relative frequency of landing on caterpillar is 0.24 . The relative frequency of landing on chrysalis is 0.3 . The relative frequency of landing on adult is 0.26 . All the outcomes cannot be considered equally likely.
Examples
Understanding relative frequencies is useful in many real-world scenarios. For example, if a company is launching a new product with different flavors, they might conduct a survey to see which flavors people prefer. The relative frequency of each flavor being chosen can help the company decide how much of each flavor to produce. This ensures they meet customer demand and minimize waste.
The relative frequencies for each stage of the monarch butterfly are as follows: egg is 0.2, caterpillar is 0.24, chrysalis is 0.3, and adult is 0.26. Since these values are not equal, the outcomes cannot be considered equally likely. Therefore, Mariah's spinner results show that some stages are more likely to be selected than others.
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