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Mathematics

Statistics

Q1
The local pizza take away randomly sampled seven customers on a Friday night and
recorded the number of pizzas they ordered. The following data were obtained
20
3
2
6
1
3
3
(a) Compute the mean, median and modal number of pizzas ordered.
(b) Which of the above measures in (a) is the most representative? Justify your
answer. (max 100 words)
(c) Compute the range, variance and standard deviation of the number of pizzas
ordered.
Q2
A manufacturer of a popular chocolate bar measures the weight of forty randomly
selected bars at the end of the production line. The weights (in grams) are
summarised in the following table:
(a) Write a summary report for the manufacturer about the performance of the
production line in terms of the weight of the chocolate bar produced. (Max 200
words) You are not required to comment on the shaded sections of the table.
(b) The bars have a weight of 50g marked on their wrappers. Do the data suggest
that the manufacturer is satisfying this requirement? Justify your decision using the
Empirical Rule.
Q3
A client has asked an investment adviser to report on the price/earnings ratios (P/E)
of 30 selected companies. The data were summarised using a stem-and-leaf display
and a Boxplot.
(a) Write a short report for the client on the price/earnings ratios of these
companies. (Max 200 words)
Q4
The shelf life of a cake mix has a mound-shaped distribution with a mean of 275
days and a standard deviation of 55 days.
(a) What percentage of cake mix packets remain fresh for 330 days or more?
(b) Find the Z-score of a cake mix packet that remains fresh for 160 days. Comment
on the relative position of this packet in the distribution.
Q5
One thousand households in a city were surveyed to see if they will subscribe to a
new pay television connection. The households were also classified as; low, medium
or high income and the data are reported in the table below:
Will Subscribe
Low Income
Medium Income
High Income
Yes
30
140
100
No
170
460
100
A household is selected at random from this population.
(a) What is the probability that the household is a medium income household?
(b) What is the probability that the household will subscribe to a new connection?
(c) What is the probability that the household will not subscribe and has a low
income level?
(d) What is the probability that the household will not subscribe or has a low income
level?
(e) What is the probability that the household has a medium income if the household
indicates it will subscribe to a new connection?
(f) Are the events “the household has a medium income” and “the household
indicates it will subscribe to a new connection” independent? State the reasons for
your answer.
(g) Are the events “the household has a low income level” and “the household will
not subscribe” mutually exclusive? State the reasons for your answer.
Q6
A large sample of over-50-year-old males was classified according to their health
status and the adequacy of their retirement savings. The sample had 55% classified
as being in poor health (P) and the rest were in good health (G). Of those in poor
health, 30% were not saving adequately for retirement (N) and 80% of those in good
health were saving adequately for retirement (S).
(a) Construct the probability tree for this problem and calculate all the joint
probabilities.
(b) What is the probability that a randomly selected person is not saving adequately
for retirement?
(c) What is the probability that a randomly selected person is in good health given
they are not saving adequately for retirement?
...

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Anonymous

Very useful material for studying!