Section outline

  • What does buying insurance or taking out a loan at the local bank have to do with statistics? What does predicting the weather have to do with probability? Why do boys generally pay more for car insurance than girls? Stay tuned, after this section and the exercises below, we will return to these questions and discuss the answers.
    ::购买保险或在当地银行贷款与统计数字有什么关系?预测天气与概率有什么关系?为什么男孩通常比女孩多支付汽车保险?在下面的这一部分和练习之后,我们将继续关注这些问题并讨论答案。

    Everyday Uses of Probability and Statistics
    ::概率和统计的日常使用

    Nearly every kind of business can benefit from an application of statistics. By knowing what product to sell at a particular time of year, or to a particular customer, a business can make the best use of product placement and advertising. Knowing what time(s) of the day, week, or year are the busiest, a manager can efficiently schedule her employees so as not to waste labor costs.
    ::几乎所有类型的企业都可以从统计应用中受益。 通过知道在特定时间销售什么产品,或者销售给某个客户,企业可以最佳地利用产品布置和广告。 了解一天、一周或一年的时间最繁忙,管理人员可以有效地安排员工时间,以避免浪费劳动成本。

    lesson content

    One type of business that makes extensive use of statistics is insurance sales. Insurance companies are just like most companies from the standpoint that they are in business to make a profit for their investors. That does not mean that buying insurance is a bad idea for individual people, or that the companies deliberately overcharge their customers, but it does mean that the companies are very careful to charge enough for each policy to ‘insure’ that the company makes money overall.
    ::广泛使用统计数据的一类企业是保险销售。 保险公司与大多数公司一样,其观点是它们为投资者谋利。 这并不意味着购买保险对个人来说是一个坏主意,也不意味着公司故意向客户收取高额费用,但确实意味着公司非常小心谨慎地收取足够多的保单费用,以“保证”公司总体上赚钱。

    How can the companies know for certain how many people are going to make claims against their insurance policies? Or how big their claims will be? They can't know for certain since they don’t have a way to see the future, but they can get a very reliable idea of the average number of claims from a specific population of people through the use of sample groups and the application of probability and statistics.
    ::公司如何知道有多少人会对其保险单提出索赔? 或他们的索赔有多大? 他们无法肯定,因为他们没有办法展望未来,但是他们可以通过使用抽样组和应用概率和统计数字,非常可靠地了解特定人口的平均索赔数量。

    Real-World Application: Profit 
    ::真实世界应用程序:利润

    Suppose a particular insurance company has 100,000 clients, and research suggests that 1 out of each 25 people are likely to make a claim in a given year, for an average of $15,000 per claim. Would a yearly premium of $750 result in a profit for the company, given these statistics?
    ::假设某个保险公司有10万客户,而研究表明,每25人中就有1人可能在某一年提出索赔,每件索赔平均为15 000美元。 根据这些统计数字,如果年保费为750美元,是否会给该公司带来利润?

    Essentially, since 1 out of each 25 people will cost the company $15,000, the total premiums for each 25 people need to be greater than $15,000 for the company to make a profit.
    ::基本上,由于每25人中就有1人将花费公司15 000美元,每25人的保险费总额必须超过15 000美元,公司才能获利。

    In other words, each policy is responsible for 1 25 t h  of $15,000, so each policy needs to cost more than :
    ::换句话说,每项政策要承担15 000美元的125美元,因此每项政策的成本必须超过:

    $ 15 , 000 25 = $ 600

    Since the company plans to charge $750 per year for each policy, that should result in a profit of $150 per policy on average, for a total estimated profit of  $ 150 × 100 , 000 = $ 15 , 000 , 000  Not bad!
    ::由于该公司计划每年为每项保单收费750美元,这应导致每保单平均利润150美元,估计总利润为150x100 000美元=15 000 000美元,不坏!

    Of course, that level of profit is only likely if the original research and statistical calculation of $15,000 per 25 people is correct (and the company has no other expenses – which is unlikely), so you can bet that huge multi-million dollar companies are very careful to make sure their calculations are as accurate as possible!
    ::当然,只有最初的每25人15 000美元的研究和统计计算正确(而且公司没有其他开支 — — 这是不太可能的 — — ),利润水平才可能达到这一水平。 因此,你可以打赌,巨资数百万美元的公司非常谨慎,以确保尽可能准确地计算!

    Real-World Application: Predicting Weather 
    ::真实世界应用:天气预报

    Predicting the weather is a tricky job. There are a nearly infinite number of possible variables that can affect the temperature and chance of precipitation for any given day. Of course, a weatherman cannot possibly take all of these variables into account every time he/she makes a prediction, so he/she must identify the most influential variables and just watch them closely for each prediction. Suppose that according to records, it has rained an average of 5 days during the month of April for each year over the last 15 years. If it is currently April 25 t h  and there has been no rain, should the weatherman warn everyone to bring an umbrella to work for the next five days?
    ::预测天气是一件棘手的工作。 几乎有无数的可能变量可以影响某一天的温度和降水机会。 当然, 天气人不可能每次作出预测都考虑所有这些变量, 所以他/ 她必须确定最有影响力的变量, 并仔细观察这些变量的预测。 假设根据记录, 在过去15年里, 4月份平均每年降雨5天。 如果现在是4月25日, 没有下雨, 天气人应该警告每个人, 带伞来工作五天吗 ?

     Maybe. However, the information regarding the average number of rainy days in April over the last 15 years probably won't have much to do with it. Although the history may be suggestive of a particular number of rainy days, it is certainly no guarantee of a specific result. If the weather conditions such as temperature, cloud cover, relative humidity, etc., are all conducive to rain, then he/she is likely to predict rain, but the fact that there are only five days left is certainly no assurance that there must be rain all five final days so that the average will be fulfilled.
    ::然而,关于过去15年中4月平均雨天数的信息可能与过去15年没有多大关系。 虽然历史可能暗示了一定数量的雨天,但肯定不能保证具体结果。 如果温度、云层覆盖、相对湿度等天气条件都有利于降雨,那么他/她可能预测降雨量,但仅剩下5天就肯定不能保证最后5天必须下雨才能达到平均雨量。

    Real-World Application: Car Insurance 
    ::现实世界应用:汽车保险

    Suppose a car insurance company reviews the police records for thousands of speeding tickets and minor car accidents over a ten-year period, and notes the following:
    ::假设一汽车保险公司在十年内审查数千张超速罚单和小车祸的警方记录,并指出如下:

      Speeding Tickets “Fender Benders ”
    Boys ages 16 - 23 4,532 1,725
    Girls ages 16 - 28 1,242 1,715

    Would it make sense for the company to charge the same rates for boys and girls?
    ::公司对男童和女童收取同样的费率是否合理?

     It certainly does not look like it.
    ::它当然不象它。

    According to the statistics, boys are nearly four times as likely to drive over the speed limit, and although there were slightly fewer recorded accidents for girls than boys, note that the age range for the girls was greater than for the boys. The greater age range suggests that there may have been more girls actually driving than boys, yet they ended up in nearly the same number of accidents!
    ::根据统计,男孩驾车超过速度限制的可能性几乎是男孩的四倍,尽管记录到的女孩的事故比男孩略少,但注意到女孩的年龄范围比男孩大。 年龄范围越大,女孩实际驾车人数可能比男孩多,但最终造成的事故数量几乎相同。

    However, it is extremely important to note that without data regarding the actual number of boys and girls in each group, we can't really get a good feel for the overall increased likelihood of boys making claims.
    ::然而,最重要的是要指出,如果没有关于每个群体中男女儿童实际人数的数据,我们无法真正对男孩提出权利主张的可能性总体增加产生良好的感觉。

    Earlier Problem Revisited
    ::重审先前的问题

    What does buying insurance or taking out a loan at the local bank have to do with statistics?
    ::购买保险或在当地银行贷款与统计数字有什么关系?

    It should make sense now to think that the interest rate you pay for a loan or the premium you pay for insurance is likely based to a great degree on what the statistics say about your likelihood to pay the loan off in a timely manner or make a claim against your policy.
    ::现在应该有理由认为,你为贷款支付的利率或为保险支付的保险费很可能在很大程度上基于统计数字中关于你能否及时偿还贷款或对保险政策提出索赔的说法。

    What does predicting the weather have to do with probability?
    ::预测天气和概率有什么关系?

    Now we know that there are a number of different variables associated with the weather, including: historical weather patterns, current temperature and local trends, current humidity, regional weather patterns, and many more. The greater the number of variables taken into account and the more accurate the calculations, the more likely it will be that a particular weather prediction will be correct.
    ::现在,我们知道,与天气相关的变量各不相同,其中包括:历史天气模式、当前温度和地方趋势、当前湿度、区域天气模式等等。 所考虑的变量数量越多,计算越准确,特定天气预测就越有可能正确。

    Why do boys generally pay more for car insurance than girls?
    ::为什么男孩子通常比女孩多付汽车保险费?

    Statistically, boys drive faster than girls, and get into more accidents. That does not mean, of course, that any particular driver is more of a risk than any other just based on his or her sex, but overall it does mean that it makes logical sense for an insurance to charge a premium for male teen drivers.
    ::从统计学上看,男孩开车比女孩快,事故也多。 当然,这并不意味着任何特定的驾驶员都比其他驾驶员冒更大的风险,只是基于性别,但总的来说,这确实意味着保险对男性青少年驾驶员收取保险费是合乎逻辑的。

    Examples
    ::实例

    Example 1 
    ::例1

    Which of these number(s) cannot represent a probability?
    ::其中哪一个不能代表概率?

    1. -0.00001
    2. 0.5
    3. 1.001
    4. 0
    5. 1
    6. 20%

    A probability can only be between 0% and 100% ( or between 0 and 1, as a decimal). 0% means it will not happen, and 100% means it will happen, every number between represents some shade of "it may happen". Choice "a" is negative, and choice "c" is greater than 100%, so neither is possible. 
    ::概率只能在0%到100%之间( 或者小数点时在0到1之间 ) 。 0%意味着它不会发生, 100%意味着它会发生, 而100%意味着它会发生, 中间的每一个数字代表着“ 可能发生” 的阴影。 选择“ a” 是负的, 选择“ c” 大于 100%, 因此两者都不可能发生 。

    Example 2
    ::例2

    Which types of studies below might a retail store make use of to improve sales?
    ::零售店利用以下哪类研究来改进销售?

    1. The average amount of money spent by customers of various age groups
      ::不同年龄组的顾客平均花费的金额
    2. The type of products preferred by customers of various age groups
      ::不同年龄组客户喜欢的产品类型
    3. The best and worst selling products to female and male customers
      ::向男女客户销售产品的最佳和最差的产品
    4. The busiest season for selling a particular product
      ::销售特定产品最繁忙的季节
    5. All of the above
      ::A. 以上所有情况

    "5" is correct. All of those bits of information would be very useful to a skilled retail manager, owner or salesperson (particularly if paid on commission).
    ::“ 5” 是正确的。 所有这些信息对熟练的零售经理、 业主或销售员( 特别是佣金支付) 非常有用 。

    Example 3
    ::例3

    How could an understanding of statistics benefit you on university entrance exams, such as ACT or SAT?
    ::在大学入学考试中,如青蒿素综合疗法或SAT考试,如何了解统计数据对您有益?

    SAT/ACT preparation courses make extensive use of statistics to help students understand when to expect a problem to be easy or hard, when it is worth spending extra time solving a particular question, and when it is not.
    ::SAT/ACT准备课程广泛利用统计数据,帮助学生了解何时希望问题容易或困难,何时值得花更多时间解决某个具体问题,以及何时不能解决问题。

    Review 
    ::回顾

    1. What is the difference between probability and statistics?
      ::概率和统计之间的差别是什么?
    2. What are three industries that make use of statistics?
      ::使用统计数据的三个行业是什么?
    3. Why do  females generally pay less for car insurance?
      ::为什么女性的汽车保险费用一般较低?
    4. Why do retail stores start carrying holiday decorations and promoting gifts well before the holiday season?
      ::为什么零售商店会在节假日之前很早就开始携带节日装饰品和促销礼品?
    5. When an animated film is played in theaters, why is it often preceded by previews of children’s movies?
      ::当一部动画片在戏剧中播放时, 为什么在电影之前常常会预览儿童电影呢?
    6. Why are commercials for toys played during cartoons?
      ::为何在漫画中播放玩具广告?
    7. Why are children’s athletic shoes often promoted by professional sports players?
      ::为什么儿童运动鞋经常由专业体育运动员推广?

    Review (Answers)
    ::回顾(答复)

    Click to see the answer key or go to the Table of Contents and click on the Answer Key under the 'Other Versions' option.
    ::单击可查看答题键, 或转到目录中, 单击“ 其他版本” 选项下的答题键 。