AP StatisticsName: ______

Test 1 (Probability and Data Analysis)Block: ______

Be sure to show all of your work.

  1. There are 8000 men and 10000 women attending a state university. If 43 percent of men and 27 percent of women are business majors, use this information to determine if the events of being a man and being a business major are independent.
  1. A travel agent books passages on three different tours, with half her customers choosing tour , one-third choosing , and the rest choosing . The agent has noted that three-quarters of those who take tour return to book passage again, two-thirds of those who take return, and one-half of those who take return. If a customer does return, what is the probability that the person first went on? (Include the probability notation as part of your answer).
  1. There are two games involving flipping a fair coin. In the first game, you win a prize if you can throw between 45 percent and 55 percent heads; in the second game, you win if you can throw more than 60 percent heads. For each game, would you rather flip the coin 30 times or 300 times? Explain your reasoning for both answers.
  1. Out of the 2000 students at Lake Norman High School, 96 are currently taking AP Statistics, 92 are currently taking some form of AP Calculus, and 7 are currently taking both. Draw a Venn diagram or a two-way table that shows the above information.

(Include the probability notation as part of your answer).

  1. What proportion of students are taking both AP Statistics and AP Calculus?
  1. If a student is not taking AP Statistics, what is the chance they are taking AP Calculus?
  1. If a student is taking AP Calculus, what is the probability they are not taking AP Statistics?
  1. The following table shows the survival status and class of passengers on the Titanic when it sank.

Class / Survived / Died
First / 197 / 122
Second / 94 / 167
Third / 151 / 476
  1. Give the marginal distribution of passengers by survival.
  1. Give the conditional distribution of passengers by class given that they survived.
  1. If ,and , what is if A and B are independent?
  1. Mr. Suk has determined he is terrible at fantasy football. He has calculated that he only has an 11 percent chance of winning on any given week. Use the line from the random number table below to simulate the 16 weeks of the fantasy football season for Mr. Suk and record the wins and losses for that simulation.

969271993136809741927756788741484094190343909994772533064359

  1. A student from another AP Statistics class described a distribution the following way:

Evaluate their description of the distribution. Be sure to mention if there

is anything incorrect about the description and/or include any information that

n=31is missing.

minX=31.4

Med=251.2

maxX=345.4

  1. Use the table below to describe the distribution of heart rates for a random sample of students at LNHS.

54 / 61 / 62 / 63 / 63 / 63 / 64 / 65 / 67 / 68
70 / 70 / 71 / 71 / 71 / 72 / 73 / 73 / 74 / 74
75 / 75 / 76 / 78 / 79 / 80 / 82 / 84 / 85 / 87
89 / 91 / 92 / 93 / 93 / 95 / 97 / 98 / 103 / 110

Bonus! (These certainly don’t happen often)

Suppose the average score on a national exam is 500 with a standard deviation of 100. If each score is increased by 20 and the result is increased by 10 percent, what are the new mean and standard deviation? Be sure to justify your answer.