Question 1

The probability distribution for the number of cookies (X) in a bag is:

The mean and standard deviation of the number of nuts in a bag is:

(a) 12.1, 1.267
(b) 12.1, 1.261
(c) 12.1, 1.59
(d) 12.5, 1.708
(e) 12.5, 1.871

Questions 2 and 3 refer to the following information 

An electrical goods manufacturer knows that 10% of his electrical appliances are defective.

Question 2

If a quality control officer inspects a sample of ten (10) electrical appliances, what is the probability that one (1) is defective. Assume independent sampling.

(a) 0.1
(b) 0.5
(c) 0.3874
(d) 0.3487
(e) 0.7361

Question 3

The quality control officer expects to find one (1) defective appliance in each batch of ten (10) appliances. What is the probability that the quality control officer finds two or more defective appliances in a batch of twenty (20) appliances?

(a) 0.6083
(b) 0.3917
(c) 0.2852
(d) 0.6769
(e) 0.3231

Question 4

A bank receives an average of five (5) bad cheques a day. Assuming the distribution is Poisson, find the probability that the bank will receive four (4) bad cheques on a particular day.

(a) 0.8
(b) 0.1755
(c) 0.1563
(d) 0.0067
(e) 0.4096

Question 5

A bank receives an average of five (5) bad cheques a day. Assuming the distribution is Poisson, find the probability that the bank will receive three or more bad cheques over a two day period.

(a) 0.1247
(b) 0.9897
(c) 0.8753
(d) 0.9972
(e) 0.0028

Question 6

The time a student waits to catch a bus in Rockhampton varies uniformly between 2 and 10 minutes. The probability that a particular student waits more than 5 minutes is

(a) 0.5
(b) 0.2
(c) 0.375
(d) 0.625
(e) 0.3

Questions 7 to 9 refer to the following information:

A drug company manufactures bottles of medicine with an average volume of 64 millilitres. The volume per bottle has a standard deviation of 0.6 millilitres. Assume that the volume in each bottle is normally distributed.

Question 7

The probability that a bottle of medicine will contain exactly 64 millilitres is:

(a) exactly zero (0)
(b) 0.0001
(c) 0.2967
(d) 0.5934
(e) 0.5

Question 8

The probability a bottle of medicine will contain between 63.9 and 65 millilitres is:

(a) 0.48
(b) 0.4525
(c) 0.115
(d) 0.9525
(e) 0.52

Question 9

Ten percent (10%) of bottles will contain more than X millilitres of medicine. The value of X is:

(a) 63.23 ml
(b) 64.24 ml
(c) 64.76 ml
(d) 63.76 ml
(e) 65.0 ml

Question 10

A television network claims that its current affairs program regularly attracts 34% of the total viewing audience. If 400 people, who were watching television at this time, were randomly surveyed, what is the probability that 150 or more people were watching the current affairs program on this network. Hint: Use the continuity correction.

(a) 0.0694
(b) 0.4222
(c) 0.0778
(d) 0.4306
(e) 0.9222

Question 11

Which of the following methods is an example of non-probability sampling?

(a) simple random sampling
(b) cluster sampling
(c) systematic sampling
(d) stratified random sampling
(e) none of the above is an example of non-probability sampling

Question 12

As a result of the Central Limit Theorem,

(a) we can use the normal distribution to make probability statements about the sample mean (X) regardless of the distribution of the variable (X) in the population if and only if the sample size is large enough
(b) using the normal approximation to the binomial is always justified.
(c) we need not take random samples, just large ones
(d) we may use normal theory for inferences about the sample mean regardless of the sampling procedures used
(e) we can use small sample sizes provided we are sampling from normal populations

Questions 13 to 15 refer to the following information:

Western Electronics has been reviewing employee absenteeism of its large workforce. During the last financial year, the company recorded a mean ()μ time lost due to absenteeism per individual of 21 days and a standard deviation ()σ of 10 days.

Question 13

If 36 employee records are randomly reviewed from last financial year, what is the probability that the average absenteeism (of the sample of 36 employees) is less than 19 days?

(a) 0.4207
(b) 0.1151
(c) 0.8849
(d) 0.3849
(e) cannot be determined unless absenteeism is normally distributed

Question 14

If 16 employee records are randomly reviewed from last financial year, what is the probability that the average absenteeism (of the sample of 16 employees) is less than 19 days?

(a) 0.4207
(b) 0.7881
(c) 0.2881
(d) 0.2119
(e) cannot be determined unless absenteeism is normally distributed

Question 15

If the total number of employees in the company were 40 and a random sample of 16 employees were surveyed, then the standard error of the sample mean would be
(a) 1.961
(b) 0.625
(c) 1.581
(d) 2.5
(e) cannot be determined as n is too small (n < 30)

Questions 16 and 17 refer to the following information:

The time (in minutes) taken by an accountant to complete a standard interview for a random sample of 12 clients is as follows:

8 12 26 10 23 21 16 22 18 17 36 9

Assume that the time to interview a client is approximately normally distributed.

Question 16

The best point estimates (in minutes) of μ and σ for the variable "interview time" are respectively: (Note that you need to calculate the best point estimates of μ and σ using the random sample of 12 clients!)

(a) 18.17, 7.77
(b) 18.17, 60.30
(c) 17.5, 8.11
(d) 18.17, 8.11
(e) Cannot be determined as the sample size is too small (ie. n < 30)

Question 17

The 98% confidence interval for μ, the mean interview time (in minutes), is:
(a) (11.81, 24.53)
(b) (14.97, 21.36)
(c) (12.07, 24.26)
(d) (0, 65.48)
(e) cannot be determined as n < 30

Question 18

In a mathematics test, a random sample of 2025 sixth graders had a mean score of 68.1 and a standard deviation of 9. Calculate the 95% confidence interval for the population mean.

(a) (67.7, 68.5)
(b) (67.9, 68.3)
(c) (50.5, 85.7)
(d) (59.1, 77.1)
(e) cannot be calculated unless test score is normally distributed

Question 19

In examining a simple random sample of 100 sales invoices from a very large number of such invoices for the previous year, an accountant finds that 65 of the invoices involved customers who bought less than $2000 worth of merchandise from the company during that year. The 90% confidence interval, for the proportion of all sales invoices that were for customers buying less than $2000 worth of merchandise during the year, is :

(a) 0.65 ± 0.004
(b) 0.65 ± 0.093
(c) 0.65 ± 0.123
(d) 0.65 ± 0.078
(e) cannot be calculated as the population size (N) is unknown

Question 20

A bulb manufacturing company wishes to calculate a 95% confidence interval for the proportion of bulbs that burn out when electricity is first applied. To produce an interval that is less than 0.02 in width, what sample size should be selected if the manufacturer wishes to be conservative.

(a) 601
(b) 38,416
(c) 9,604
(d) 2,401
(e) 25