Question One

(i) Differentiate between parameter and statistic

(ii) Explain four types of scales of measurement in statistical analysis.

(iii) It is said that secondary data should be used with utmost care. Explain three characteristics of secondary data that a statistical investigate must observe before using them.

(iv) What are the differences between a histogram and a bar plot.

(v) A car salesman takes inventory and finds that he has a total of 125 cars to sell. Of these 97 are the 2001 model, 11 are the 2000 model, 12 are the 1999 model and 5 are the 1998 model.

(a) Which two types of charts are most appropriate to display the data?

(b) Construct the charts.

Question Two

(i) The mean weight of 800 male students at a certain college is 140kg and the standard deviation is 10kg assuming that the weights are normally distributed find how many students weigh

(a) between 130 and 148kg

(b) more than 152kg

(ii) On experience, it is found that an executive is late for office on four days out of 30 working days. Let X denote the number of times that the executive will be late to the office in the next 60 working days. Determine P(5 X 10)

(iii) A gumball machine has gumballs of five flavors. There are 10 apple, 15 berry, 12 cherry, 8 orange, and 9 mint. When a quarter is put into the machine, it dispenses 5 gumballs at random. What is the probability that each gumball is a different flavor?

Question Three

(i) Suppose the mean monthly return on a T-Bill is 0.5% with a standard deviation of 0.58%. Suppose we have another investment Y with a 1.5% mean monthly return and standard deviation of 6%. Which of the two investments offers less risk in terms of investment.

(ii) Make a frequency distribution table for the data on mileage ratings using 5 intervals (five classes) of equal length. Include the left end point of each interval and omit the right end point.

36.3 41.0 36.9 37.1 44.9 40.5 36.5 37.6 33.9 40.2 38.5 39.0 35.5 34.8 38.6 41.0 31.8 37.3 33.1 37.0 37.1 40.3 36.7 37.0 33.9

(iii) Use your table in (i) to answer the following questions

(a) Construct a well labeled histogram and estimate the mode of the distribution.

(b) Construct a well labeled cumulative frequency curves (ogive) and estimate the median and the quartiles of the distribution.

(iv) A student's final grades in mathematics, physics, chemistry and sports are, respectively 82, 86, 90 and 70. If the respective credits received for these courses are 3, 5, 3 and 2, determine an appropriate average grade.

Question Four

(i) A parking building which is open for 7 hours a day has the following fee policy: 18 dollars per hour for the first 3 hours of parking and 6 dollars for each additional hour. Many years of data shows that the number of hours of parking for a car, denoted X, is a discrete random variable with probability function

P(X = x) = {(8 k)/28 , for k = 1, 2, , 7

0, otherwise}.

What is the mean parking charge for a car in dollars under this policy? What is the corresponding standard deviation?

(ii) A continuous random variable X has a pdf f(x) given by

f(x) = {k(x 2 2x + 2), 0 < x 3,

3k, 3 < x 4,

0, otherwise.}

(a) Show that k = 1 /9

(b) Find the P(2 X 3.8)

(c) Find the mean of X and its corresponding standard deviation.