Basic Statistics > A-Level Question Paper > Sophia Statistics Milestone 3 (All)

Sophia Statistics Milestone 3

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Kyle was trying to decide which type of soda to restock based on popularity: regular cola or diet cola. After studying the data, he noticed that he sold less diet cola on weekdays and weekends. However, after combing through his entire sales records, he actually sold more diet cola than regular cola. Which paradox had Kyle encountered? Benford's Law False Negative Simpson's Paradox False Positive RATIONALE This is an example of Simpson's paradox, which is when the trend overall is not the same that is examined in smaller groups. Since the sale of diet coke overall is larger but this trend changes when looking at weekend/weekday, this is a reversal of the trend. CONCEPT Paradoxes 2 Luke went to a blackjack table at the casino. At the table, the dealer has just shuffled a standard deck of 52 cards. Luke has had good luck at blackjack in the past, and he actually got three blackjacks with Queens in a row the last time he played. Because of this lucky run, Luke thinks that Queens are the luckiest card. The dealer deals the first card to him. In a split second, he can see that it is a face card, but he is unsure if it is a Queen. What is the probability of the card being a Queen, given that it is a face card? Answer choices are in a percentage format, rounded to the nearest whole number. 33% 4% 77% 8% RATIONALE The probability of it being a Queen given it is a Face card uses the conditional formula: Note that there are 12 out of 52 that are face cards. Of those 12 cards, only 4 of them are also Queens. CONCEPT Conditional Probability 3 Which of the following situations describes a continuous distribution? A probability distribution of the workers who arrive late to work each day. A probability distribution of the average time it takes employees to drive to work. A probability distribution showing the number of minutes employees spend at lunch. A probability distribution showing the number of pages employees read during the workday. RATIONALE For a distribution to be continuous, there must be an infinite number of possibilities. Since we are measuring the time to drive to work, there are an infinite number of values we might observe, for example: 2 hours, 30 minutes, 40 seconds, etc. CONCEPT Probability Distribution 4 Which of the following is a condition of binomial probability distributions? All observations made are independent of each other. All observations are mutually exclusive. All observations made are dependent on each other. All observations are made randomly.

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