statistical analysis

Normal distributions

Records from a call centre show that over a long period of time, waiting times for callers

are normally distributed with a mean of 2.5 minutes and a standard deviation of 1.7

minutes. Sketch the normal curves and calculate the probabilities in Questions 14 to 16.

Question 1

Find the probability that a randomly selected caller waits longer than 3 minutes. Round

z-value to 2 decimal places but retain 4 decimal places for your probability.

Question 2

Find the probability that a randomly selected caller waits between 1 and 2 minutes.

Round z-value to 2 decimal places but retain 4 decimal places for your probability.

Question 3

Find the length of waiting time exceeded by 30% of all callers. Express your final answer

to 2 decimal places.

Design of experiments

The head of the quality control department at a publishing company is studying the

effect of type of glue and type of binding on the strength of the bookbinding. The

company has three possible glues to choose from and the book can either be bound as a

paperback or a hardback.

Question 4

Write a short paragraph outlining an experiment to address the question of which

combination of glue and binding is most effective and show this on a diagram. Explain

how the principles of experimental design are met.

Question 5

How many factors are there? Name them.

How many treatments are there? Name them.

Describe a suitable response variable and how it could be measured.

Section E: Sampling design

Human resources staff wish to survey a sample of workers from the StaffDetails data set

to see how they view the health and fitness facilities and activities available in their

workplace.

Question 6

Use software to generate a simple random sample of 30 workers from StaffDetails. Take

the screenshot of the software screen where you defined your simple random sample.

Insert this screenshot in your report. List the ID numbers of those selected.

Question 7

Describe two other sampling methods which could be used to obtain a sample from this

population. What advantages or disadvantages does each method have?

SECTION F: Probability

Using the StaffDetails data, draw up a two-way table showing the number of people in

each location by position. Questions 17 to 21 relate to this table. Round all probabilities

to 2 decimal places.

Question 8

What is the probability that a randomly selected person works in the Christchurch office?

Question 9

State the complement rule and use it to find the probability that a randomly selected

person is not in the Christchurch office.

Question 10

Name two events (one position and one location) which are disjoint.

Question 11

State the addition rule for disjoint events and use it to find the probability that a

randomly selected person is a professional or a specialist.

Question 12

From your table find the probability that a randomly selected person is a specialist in

Dunedin. Check to see if the two events {the person chosen is a specialist} and {the

person is from Dunedin} are independent using the multiplication rule for independent

events.