Q. 1

If a fair coin is tossed 100 times, use the normal curve to approximate the probability that the number of heads is between 45 and 55.

Q. 2

A sample of 26 offshore oil workers took part in a simulated escape exercise, resulting in the accompanying data on time (sec) to complete the escape. A stem-and-leaf display of this data appears below:

32 55 stem: ones

33 49

34

35 6699

36 34469

37 03345

38 9

39 2347

40 23

41

42 4

a) Calculate the values of the sample mean and median.

b) By how much could the largest time be increased without affecting the value of the sample median?

c) By how much could the largest time be decreased without affecting the value of the sample median?

d) What are the values of the sample mean x and sample median x when the observations are re-expressed in minutes?

e) What are the values of the sample standard deviation and quartile 1 and quartile 3.

f) Comparing the mean and the median, what skew does the distribution have?

Q. 3

A mail-order computer business has six telephone lines. Let x denote the number of lines in use at a specified time. Suppose the mass function of x is given by

x: 0 1 2 3 4 5 6

p(x): 0.1 0.15 0.20 0.25 0.20 0.05 ?

a) What is the missing probability when x = 6 telephone lines.

b) Calculate the value of the mean of x.

c) Calculate the value of the standard deviation of x.

d) What proportion of this computer business will have at least 3 telephone lines in use?

e) What proportion of this computer business will have at most 5 telephone lines in use?

f) For what proportion of this computer business will the number of telephone lines in use be within 1 standard deviation of the mean value?