Answer all if possible and show your workings.

Questinnl (a) In a certain Pick 4 game, you pay R51 to select a sequence of four digits. such as 2283. If you buy only one ticket and win. your prize is Rs 5000 and your net gain is 4999. We assume that a sequence can be played only once for a draw. (i) Suppose you buy one ticket. Determine the probability of winning. (ii) Construct a table describing the probability distribution and outcomes corresponding to the purchase of one Pick 4 ticket. (iii) If you play this game once every day. determine the mean number of wins in years with exactly 365 days. (iv) If you play this game once every day. determine the probability of winning exactly once in 365 days. (v) Determine the expected value for the purchase ot one ticket. (vi) Determine an expression for the probability of winning it you buy 5 tickets every day for 365 days. (vii) Determine an expression for the probability of winning up to 10 times it you buy 5 tickets every day tor 365 days. [2+2+2+2+2+2+2 marks} (bl In a survey of a recent IS promotion. ex- students were asked it they owned their own home. rented an apartment / house. or lived with their parents. The table below shows the res . - nses: w Parents _I__ __ (i) Determine the probability of selecting one ex-student from this promotion and getting a male who owns his own home. (ii) Determine the probability that one ex-student is selected and that ex-student is a renter given that the ex-student is known to be a male. [2+4 marks: Question 2 (a) A big company in the IT sector has 329,373 employees and 637.133 stockholders. A vice president plans to conduct a survey to study the numbers of shares held by individual stockholders. (i) State with justification whether the numbers of shares held by stockholders discrete or continuous (ii) Identify the level of measurement (nominal, ordinal. interval, ratio) for the numbers of shares held by stockholders. (iii) If the survey is conducted by telephoning 20 randomly selected stockholders in fifty (50) countries. determine with justification, what type of sampling (random, systematic. convenience. stratified, cluster) is being used. ; _ _---: (iv) It a sample of 1000 stockholders is obtained. and the average (mean) number of shares is calculated for this sample. determine whether the result is a statistic or a parameter. (v) Discuss about the appropriateness of a survey. to get an idea of stockholders views about employee benefits. by mailing a questionnaire that stockholders could complete and mail back. [2+2+2+2+2 marks] (b) The number of credits completed by a sample of 53 IS students is shown below: 9991212121218181819202730303335353739394243434547 50 50 52 5356 57 5757 6064 656670 72 73 76 76 80849092 103 106 109 109 120 120 Use the information to respond to the totlowing questions: (i) We want to create a frequency distribution with five classes. Determine the class width to be used as well as the frequency corresponding to each class. (it) Construct a relative frequency distribution for this data. (iii) Construct a cumulative frequency distribution for this data. (iv) Construct a frequency polygon for this data. Use your answer book for this purpose. [2+2+2+4 marks}