25. (a) Use Table 1 in Section 10 of this Unit Guide, to find the following probabilities:
(i)
(ii)
(iii)
P(Z 0.4)
P(Z <1.52)
P(Z 1.94)
(iv)
(v)
(vi)
P(Z 1.96)
P(Z >1.96)
P(0 < Z <1.28)
(b) Use Table
17. The owner of an appliance store is interested in the relationship between the price at
which an item is sold (retail price or sale price) and the customers decision on whether
or not to purchase a
Solutions to tutorial problems 17-21: Probability
17. (a)
(i)
Table of probabilities obtained by dividing through by
2000:
W
W
R
(ii)
0.21
0.14
0.57
0.08
R
Including marginal probabilities (row and co
22
(a)
Probabiity distribution for number of absences
0.3
0.25
Probability
0.2
0.15
0.1
0.05
0
0
1
2
3
4
5
6
7
Number absent
Bar chart used, since this is a quantitative discrete variable.
As well as
Solutions to tutorial questions 28 31
28.
Let X be the random variable length of component. Then X ~ N (117,2.1) .
(units of cm)
X 117 120 117
3
(i) Pr( X 120) Pr(
) Pr(Z
)
2.1
2.1
2.1
where Z is a s
Tutorial 9 solutions
Solutions to tutorial questions 35 38
35. Limits of 95% confidence interval:
14.9
s
x t 2
= 156.3 t0.025
12
n
where the critical value of t is taken from the distribution with 11
Tutorial 8 solutions
Solutions to tutorial questions 32 34
32. Let be the population mean annual income.
(a) We are asked to see if we can prove that the management negotiator is correct, so we
are lo
Tutorial 10 solutions
Regression solutions 39 40
Question 39.
(a) There appears to be a positive linear relationship. There is also considerable random variation
around the values on the line of best
Tutorial 3 solutions questions 15 16
15. Note that in this ogive, the classes are 14 24, 24 34, etc.
Ogive of age distribution of divorced people in Australia, 1997
and 2001
percentage of divorced per
Questions 8 - 11
8.
Suppose that n = 3, x1 = 5, x2 = 8, x3 = 14, y1 = 7, y2 = 3 and y3 = 8.
Evaluate the following:
3
(a)
3
(b)
xi
i 1
(d)
i 1
3
3
(xi 9)
(e)
i 1
(g)
i 1
xi yi
i 1
(xi 9)
2
(f)
i
12. A survey of the number of non-family employees of 132 small businesses in the town of
Shallowhaven yields the following results:
Number of employees
0
1
2
3
4
5
Frequency
35
31
33
13
17
3
(a) For
22. The manager of manufacturing at the Afford Motor Company is concerned about the
absenteeism of assembly line employees. Using historical data, he obtained the
following probability distribution of
28. Selvanathan et al., p.405, 10.14.
An automatic machine in a manufacturing process is operating properly if the lengths of
an important subcomponent are normally distributed, with mean = 117 cm and
15. The ogive shows the percentage of divorced persons who are younger than the age
specified on the x axis, for 1997 and 2001. Note: the class boundaries are 14, 24, 34
etc.
(a) Interpret the fact th
32. During Enterprise Bargaining negotiations between management and unions, the
management negotiator argues that the companys building workers who are paid an
average of $50,000 per year, are well p
35. Selvanathan et al., p.450, 11.37.
You are given the following statistics: x 156.3, s 14.9, n 12 .
Estimate the population mean with 95% confidence.
What assumption must be made to answer this ques
44. Two forecasting procedures were applied to the series in Excel Ex34 in order to forecast
the sales for the four quarters of 2006. The forecasts and the actual sales are given in
the following tabl
41. For the following graphs of time series, comment on what components appear to be
present. Is it possible to decide if the components should be combined additively or
multiplicatively?
Price of win
Exercise 31: Regression using Excel
Adapted from Selvanathan et al., Exercise 14.20. Data in Exercise31_33.xls
See section 7.5.3 of this unit guide for instructions on how to use the Regression tool i