Question 1 a) Choose the most appropriate term that describes the following i. The number of vaccinated citizens in a country [discrete, continuous] ii. The faculty that a student registers in [qualitative, quantitative] iii. The volume of water a kettle can hold [interval, ratio] b) Caitlyn has to determine how many of the 120 employees in her work place has comprehensive car insurance. She wants to obtain a sample of 40 employees. She selections employees from each department in proportion to the number of individuals the departments i. Dene the term population with relation to the question above. ii. What type of sampling method did Caitlyn use? iii. List two advantages of the sampling method stated in ii). iv. Below are the number of individuals in each department How many employees from the Marketing department should Caitlyn select to be part of the sample? * v. Another employee suggested that Caitlyn should group employees by the type of car they own. State a reason why grouping the employees in this way will NOT be appropriate to select this sample using the sampling method in EB Question 2 The cumulative frequency table below shows the marks earned by 1400 students in Mathematics and English 1500 1400 1300 1200 1 100 English Mathematics 1000 900 800 Cumulative frequency 700 600 500 400 300 200 100 10 20 30 40 50 60 70 80 90 100 Marks Using the graph above 1. How many students got more than 40 marks in mathematics? ii. How many students got between 60 and 70 marks in English?iii. Use suitable data from these graphs, use the median and interquartile range to compare the marks in Mathematics and English. I b) The number of planes to arrive at the Dubai International Airport over N days were recorded and inputted into MINITAB for analysis. Exhibit 1 was subsequently generated. Exhibit 1 Stem-and-Leaf Display: No. of Arrival Leaf Unit = 1 N =* 5 2 01123 10 2 56899 ** 3 0001123 (***) 3 6666678888 12 4 01134 7 4 57789 2 5 00 i. Calculate he missing values *, *"' and **"' ii. Find the value ofthe a) Median b) Highest value c) Mode c) Using the stern and leaf diagram in Exhibit 1, i. Form a frequency table by identifying the class intervals implicitly.\" Using the table created in 2ci) above, ii. Calculate the sample mean iii. Calculate the sample variance lestion 3 a) Two events, M and N, are such that P(M) = 0.6, P(M nN) = 0.2, P(M UN) = 0.85 Find (i) P(N |M) State, with reason, whether M and N are (11) mutually exclusive (iii) independent. b) The following table shows the results of a sample survey carried out by a fast-food restaurant to determine whether persons had noticed an improvement in its service in the last month Voting Results Sex Improvement No No Seen improvement Opinion Male 25 21 34 Female 16 38 16 1 . How many people were in the survey? ii. A patron was selected at random from the sample. a) Determine the probability that the patron thought that there was an improvement in service. b) Determine the probability that the patron was a female or thought that there was no improvement in the service. c) Given that the patron thought there was an improvement, what is the probability that the patron was a male? End of Assessment #1
