Level 3 Level 2 Level 1 Introduction (http://www.nzqa.govt.nz/qualifications-standards/qualifications/ncea/understanding-ncea/the facts/factsheet-4/) The chart below shows the distribution of credits gained during 2010 by year 11, 12 and 13 students. Subject Reference Mathematics and Statistics Title Level Credits Apply xxxxxxxx in solving problems. Assessment Achievement Achievement with Merit Apply xxxxxxxx in solving problems. Internal/external Achievement with Excellence Apply xxxxxxxxxxx, using relational thinking, in solving problems. Apply xxxxxxxxxxx, using extended abstract thinking, in solving problems. . Level 1 Level 2 AS91026 1.1 Apply numeric reasoning in solving problems AS91256 Apply co-ordinate geometry methods in solving problems 4 credits 2 credits Internal AS91027 1.2 Apply algebraic procedures in solving problems Internal AS91257 Apply graphical methods in solving problems 4 credits 4 credits External (CAT) Level 3 2.1 3.1 Apply the geometry of conic sections in solving problems 3 credits Internal 2.2 3.2 Apply linear programming methods in solving problems 2 credits Internal AS91028 1.3 Investigate relationships between tables, equations and graphs Internal AS91258 Apply sequences and series in solving problems 2.3 3.3 Apply trigonometric methods in solving problems 4 credits 2 credits External AS91029 1.4 Apply linear algebra in solving problems Internal AS91259 2.4 Apply trigonometric relationships in solving problems 3 credits 3 credits 4 credits Internal 3.3 Apply trigonometric methods in solving problems 4 credits Internal Internal AS91030 1.5 Apply measurement in solving problems AS91260 Apply network methods in solving problems Internal 3 credits 2 credits Internal AS91031 1.6 Apply geometric reasoning in solving problems Internal AS91261 Apply algebraic methods in solving problems 4 credits 4 credits External AS91032 1.7 Apply right-angled triangles in solving measurement problems External AS91262 Apply calculus methods in solving problems 3 credits 5 credits 2.5 3.4 Use critical path analysis in solving problems 2 credits Internal 2.6 3.5 Apply algebraic methods in solving problems 5 credits External 2.7 3.6 Apply differentiation methods in solving problems 6 credits External AS91033 1.8 Apply knowledge of geometric representations in solving problems AS91263 Design a questionnaire 3 credits 3 credits Internal Internal 2.8 3.8 Investigate times series data 4 credits Internal 3.9 Investigate bivariate measurement data 4 credits AS91034 1.9 Apply transformation geometry in solving problems 2 credits AS91264 Use statistical methods to make an inference Internal 2.9 3.10 Use statistical methods to make a comparison 4 credits 5 credits Internal AS91265 2.10 Conduct an experiment to investigate a situation using statistical methods Internal AS91035 1.10 Investigate a given multivariate data set using the statistical enquiry cycle 4 credits 3 credits 3 credits Internal AS91036 1.11 Investigate bivariate numerical data using the statistical enquiry cycle Internal AS91266 Evaluate a statistically based report 3 credits 2 credits Internal AS91037 1.12 Demonstrate understanding of chance and data Internal AS91267 Apply probability methods in solving problems 4 credits 4 credits 4 credits External AS91038 1.13 Investigate a situation involving elements of chance External AS91268 2.13 Investigate a situation involving elements of chance using a simulation External 2 credits 4 credits Internal 3 credits 3.11 Conduct an experiment using experimental design principles Internal 2.11 3.12 Critically evaluate statistically based reports 4 credits External 2.12 3.13 Apply probability concepts in solving problems 3.14 Apply probability distributions in solving problems Internal Internal AS91269 Apply systems of equations in solving problems External 2.14 3.15 Apply linear systems in solving problems A New Zealand tour company collected data over a period of a year to investigate information about its passengers. (a) It found that: • 48% of its passengers were male • 63% of its female passengers came from overseas • 21% of all passengers were males from overseas. You may assume that the event that a passenger is male and the event that a passenger is from overseas are independent. Find the probability that a randomly selected male passenger was from overseas. The tour company decides to analyse its data in more depth. (a) It finds that: • the probability of an overseas passenger coming from Australia is 2/3 • the probability of an overseas passenger coming from Australia or aged over 30 is 3/4 • the probability of an overseas passenger coming from Australia and aged over 30 is 1/10. Find the probability that an overseas passenger is aged over 30. In 2006, a survey was conducted on households in Hamilton, Canada. (a) Let the random variable X represent the number of cars in a randomly chosen household at the time of the survey. The survey gave the following probability distribution for X. x 0 1 2 3 4 P(X = x) 0.059 0.383 0.377 0.153 0.028 Find the expected value of X.