The sentence which contains a detail that best supports Rany's claim is, 'In fact, one study showed that people who identified as being happy are twelve percent more productive than their colleagues.'
Step-by-step explanation:
Randy claims that when people are happy, they are way more productive as compared to the unhappy ones. This claim can be best supported from the third sentence. It is because the sentence supports the claim by providing statistical data about the percent of productiveness found in happy people. It also clearly addresses the topic, which is turn makes Randy's research quite reliable and effective.