QUESTION ONE

a.Express log2 (x + 2) - log2 x as a single logarithm. Hence solve the equation log2 (x + 2) - log2 x = 3 (3 marks)

b.Solve the equation 22 x+1 +2x+2 =12 -2x (3 marks)

QUESTION TWO

The radio music listener market is diverse. Listener formats might include adult contemporary, album rock, top 40, oldies, rap, country and western, classical, and jazz. In targeting audiences, market researchers need to be concerned about the ages of the listeners attracted to particular formats. Suppose a market researcher surveyed a sample of 170 listeners of country music radio stations and obtained the following age distribution.

Age (years) Frequency

15-under 20 9

20-under 25 16

25-under 30 27

30-under 35 44

35-under 40 42

40-under 45 23

45-under 50 7

50-under 5 2

a.Calculate the mean and modal ages of country music listeners(8 marks)

b.Calculate the variance and standard deviation of the ages of country music listeners (4 marks)

c.Draw a cumulative frequency curve and from the graph determine the mean and interquartile range(8 marks)

(25 marks)

QUESTION THREE

A few years ago, a survey commissioned by The World Almanac and Maturity News Service reported that 51% of the respondents did not believe the Social Security system will be secure in 20 years. Of the respondents who were age 45 or older, 70% believed the system will be secure in 20 years. Of the people surveyed, 57% were under age 45. One respondent is selected randomly.

a.What is the probability that the person is age 45 or older? (5 marks)

b.What is the probability that the person is younger than age 45 and believes that the Social Security system will be secure in 20 years? (5 marks)

c.If the person selected believes the Social Security system will be secure in 20 years, what is the probability that the person is 45 years old or older? (5 marks)

d.What is the probability that the person is younger than age 45 or believes the Social Security system will not be secure in 20 years? (7 marks)

(20 marks)

QUESTION FOUR

a.Bank customers arrive randomly on weekday afternoons at an average of 3.2 customers every 4 minutes. What is the probability of having more than 7 customers in a 4-minute interval on a weekday afternoon? (6 marks)

b.A high percentage of people who fracture or dislocate a bone see a doctor for that condition. Suppose the percentage is 99%. Consider a

sample in which 300 people are randomly selected who have fractured or dislocated a bone.

(i)What is the probability that exactly five of them did not see a doctor? (4 marks)

(ii)What is the probability that fewer than four of them did not see a doctor? (5 marks)

(iii)What is the expected number of people who would not see a doctor? (5 marks)

(20 marks)

QUESTION FIVE

A study about strategies for competing in the global marketplace states that 52% of the respondents agreed that companies need to make direct investments in foreign countries. It also states that about 70% of those responding agree that it is attractive to have a joint venture to increase global competitiveness. Suppose CEOs of 95 manufacturing companies are randomly contacted about global strategies.

a.What is the probability that between 44 and 52 (inclusive) CEOs agree that companies should make direct investments in foreign countries?(4 marks)

b.What is the probability that more than 56 CEOs agree with that assertion? (4 marks)

c.What is the probability that fewer than 60 CEOs agree that it is attractive to have a joint venture to increase global competitiveness? (5 marks)

d.What is the probability that between 55 and 62 (inclusive) CEOs agree with that assertion? (7 marks)

(20 marks)