Question 1 (Marks: 10)
Q.1 Spree advertises that 90% of its online orders are delivered within five working
days. You select a random sample of 150 online orders from last month to audit and
found out that, 132 of these orders were actually shipped on time. Assuming that
this is a normal distribution:
Q.1.1 Calculate the standard error of the sample proportions. (3)
Q.1.2 Calculate the probability that more than 88% of the orders in the sample
will be delivered on time. Interpret your answer.
(7)
Question 2 (Marks: 20)
Q.2.1 The Bookworm Club has found that 30% of its members attended school in the
Johannesburg area. A sample of 145 members is randomly selected. Assuming normal
distribution:
Q.2.1.1 Determine the standard error for this sample. (3)
Q.2.1.2 What is the probability that more than 31.50% of the members of the club
attended school in Johannesburg? Interpret your answer.
(7)
Q.2.2 Experience has shown that on average, customers of the Cultured Camping website
spend R750 (μ) per purchase, with a standard deviation of R85 (σ). A sample of 95
purchases is randomly selected. Assuming normal distribution:
Q.2.2.1 Determine the standard error for this sample. (3)
Q.2.2.2 What is the probability that the mean value of the purchases in the sample is
less than R755? Interpret your answer.
(7)
Question 3 (Marks: 10)
Q.3.1 Of the 150 randomly selected mine workers interviewed, 28 indicated that they would
prefer an industrial action if they did not get a 15% increase in their salaries.
Calculate a 95% confidence interval of the proportion of mine workers who would
(10)
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prefer an industrial action.
Question 4 (Marks: 20)
Q.4.1 Construct a 99% confidence interval for the true average number of hours that
teenagers spend on social media per day, if it was found that the average number of
hours that a sample of 22 teenagers spent on social media per day was 4.25 hours,
with a standard deviation of 0.75 hours.
(11)
Q.4.2 Construct a 90% confidence interval for the true average monthly cost of renting a
one-bedroom flat in the Randpark Ridge area, if it was found that a sample of 110
different flats in the area cost an average of R5 999 per month. Assume a population
standard deviation of R1 721.25.
(