QUESTION 1 [15 MARKS]

1.1 It is known that the time it takes to mark assignments are normally distributed with a population standard deviation of 3.5 minutes. If a random sample of 81 assignments should be marked, what is the probability that the average time to mark these assignments will differ by no more than 1.2 minutes in either direction from the unknown population mean marking time? (5 marks)

1.2 The amount of time that students spend with their books per week is normally distributed with a mean of 52 hours and a standard deviation of 6 hours. 1.2.1 What is the probability that a student studies for 60 hours and more per week. (5 marks) 1.2.2 Find the probability that the mean amount of study time for three randomly selected students is 60 hours and less per week. (5 marks)

QUESTION 2[15 MARKS]

In a sample of 200 observations, we found the proportion of successes to be 48 %.

2.1 Use a 90 % degree of confidence to estimate the population proportion of successes. (5 marks)

2.2 Repeat with n = 500. (4 marks)

2.3 Repeat with n = 1000. (4 marks)

2.4 Describe the effect on the confidence interval estimate of increasing the sample size. (2 marks)

QUESTION 3 [15 MARKS]

A film-processing company claims that the owners of digital cameras store on average more than fifteen pictures on their cameras, before the eventually download these to a computer or print. A random sample of 10 digital camera owners produced the data below on the number of pictures stored on their digital cameras.

25 6 22 26 31 18 13 20 14 2

3.1)

Test this claim at the 10 % level of significance. (10 marks)

3.2) Estimate with 95 % confidence the mean number of pictures stored on digital cameras. (5 marks)

QUESTION 4 (15 MARKS)

A marketing manager at a big retail shop claims that the variance in the weights of cereal boxes are less than 0.003 kilogram 2 . Thus, the weights (in kilograms) of a random sample of eight of these cereal boxes are listed here.

1.07 .98 .95 1.05 .99 1.09 1.03 .96 4.1

Test this clam at a 1 % level of significance

(8 marks)

4.2 Estimate the variance of the entire population of cereal box weights with 90% confidence. (7 marks)