Question 1

Q.1.1 It has been found that on average, four motorbikes go through an N1 tollgate every 20 minutes. What is the probability that:

Q.1.1.1 No more than 2 motorbikes will go through the tollgate in any randomly selected 20-minute period? Interpret the answer. (5)

Q.1.1.2 More than 3 motorbikes will go through the tollgate in any randomly selected 20-minute period? Interpret the answer. (5)

Q.1.2 The time taken to complete a web-based questionnaire is normally distributed, with an average time () of 9 minutes and a standard deviation () of 1.55 minutes. What is the probability that a randomly selected person will take:

Q.1.2.1 Between 8 and 8.5 minutes to complete the questionnaire? Interpret the answer. (5)

Q.1.2.2 Between 8.75 and 9.75 minutes to complete the questionnaire? Interpret the answer. (5)

Question 2

Q.2.1 Give a definition of what is meant by the term "sampling distribution of the sample proportions". (3)

Q.2.2 Define the term "standard error". (2)

Q.2.3 Glass Houses Pty has found that the cost of fitting new sliding doors is normally distributed, with an average cost per door of R12 750, and a standard deviation of R1 095. A sample of 105 new windows is randomly selected. Assuming normal distribution:

Q.2.3.1 Determine the standard error for this sample. (3)

Q.2.3.2 What is the probability that the average cost of fitting the doors in the sample is less than R13 000? Interpret the answer. (7)

Question 3

Q.3.1 Briefly discuss the five steps in the hypothesis testing process. (5)

Q.3.2 A soft drink manufacturer claims that less than 5% of its two litre bottles are underfilled. Test this claim at the 1% significance level, if a survey found that 32 out of a random sample of 800 two litre bottles were found to be underfilled. (10)

Q.3.3 The national manager of a chain of DIY stores claims that, on average, the stores sell 1 850 pairs of overalls per month. Test this claim at the 5% significance level if it was found that over a sample of 24 months, the stores sold an average of 1 895 pairs of overalls per month, with a standard deviation of 145 pairs of overalls per month. (10)