QUESTION 1
The probability that in the next 1 000 customers, the hotel chain will have no mishandled bags can be calculated using the Poisson distribution formula:
P(X=0) = (e^-λ * λ^0) / 0!
Where λ is the average number of mishandled bags per 1,000 customers, which is 4.06 in this case.
P(0) = (e^-4.06 * 4.06^0) / 0!
P(0) = (e^-4.06 * 1) / 1
P(0) = e^-4.06
Calculating this value, we get:
P(0) = 0.0172
Therefore, the probability that in the next 1,000 customers, the hotel chain will have no mishandled bags is 0.0172.
ANSWER: 0.0172
QUESTION 2
To determine which person, X or Y, will have the most money available after exactly 17 years, we need to calculate the future value of their investments.
For Person X:
PV = 0 (no initial investment)
PMT = 150
n = 17*12 (months)
I/Y = 6/12 = 0.5 (monthly interest rate)
Calculating using a financial calculator or formula, Person X will have R 52,986 available after 17 years.
For Person Y:
PV = 0 (no initial investment)
PMT = 380
n = 17 (years)
I/Y = 9
Calculating using a financial calculator or formula, Person Y will have R 14,049.85 available after 17 years.
Therefore, Person X will have the most money available after exactly 17 years.
ANSWER: X with R 52,986
(For the remaining questions, I can provide assistance upon request)
Question Completion Status:
QUESTION 1
A major hotel chain keeps a record of the number of mishandled bags per 1 000 customers. In a recent year, the hotel chain had 4.06 mishandled bags per 1 000 customers. Assume that the number of mishandled bags has a Poisson distribution. What is the probability that in the next 1 000 customers, the hotel chain will have no mishandled bags?
0.0254
0.0687
0.0256
0.0172
0.0025
1 points
QUESTION 2
Person X invests R 150 at the end of each month with bank X who adds interest at 6% per annum, compounded monthly. Person Y invests R 380 at the end of each year with bank Y who adds interest at 9% per annum compounded annually. Who will have the most money available after exactly 17 years?
Y with R 14 049.85
X with R 52 986
X with R 4 231.93
Y with R 1 890.70
None of the above
1 points
QUESTION 3
How long will it take R14000.00 to accumulate to R28 000.00 at 18.60% simple interest per annum?
2
4.06
5.38
10.75
1 points
QUESTION 4
Consider the following two price index series:
Year 1995 = 100
2002 80
2003 86
2004 90
2005 94
Year 2000 = 100
2005 115
2006 121
2007 130
2008 133
Splice the two index series to form one continuous series with 1995 as the base year. The index for 2006 is:
95.65
94
98.90
102.28
1 points
QUESTION 5
An amount of R100 is deposited with a financial institution for two years, at an interest rate of 12% per annum simple interest. What is the accumulated amount after two years?
R24
R100
R124
R112
None of the preceding
1 points
QUESTION 6
You purchase a new flat for R 250 000, and pay R 50 000 as a down payment. You take out a loan for the remainder at an interest rate of 12% p.a., compounded monthly, for 30 years. Calculate your monthly loan payment.
R 2 986.21
R 2 057.23
R 12 552.66
R 19 942.76
R 3 805.44
1 points
QUESTION 7
A carrier of tuberculosis has a 10% chance of passing the disease on to anyone with whom he comes into close contact who has had no prior exposure. During a day, he meets 10 such individuals. Calculate the probability that less than 6 of these individuals will contract tuberculosis.
0.9
0.1
0.9437
0.9874
0.9999
1 points
QUESTION 8
Mr. Setlaba is planning to buy himself a new car in 2 years’ time. He estimates that the car will cost him R168000 and that the trade-in on his old car 2 years from now will be R 15 500. Mr. Wilson decides to open a savings account in which he wants to deposit a fixed amount every month so that he will be able to afford the car. What amount should Mr. Wilson be saving monthly if the bank will pay interest of 13.7 % per annum compounded monthly on the savings account?
R 6 132
R 75 817.84
R 5 566.25
None of the above
1 points
QUESTION 9
Harry Henn pays a fixed amount of R200 at the beginning of each month for a period of five years towards a savings plan that earns interest at a rate of 15% per annum compounded monthly. What amount will he receive from this savings plan?
R17 936.34
R1 550.75
R8 512.00
R1 532.98
R17 714.90
R1 348.48
1 points
QUESTION 10
The value of k in:
- 0.81
0.69
0.85
0.75
0.77
1 points
QUESTION 11
By using the data in the table below, for 2005 with 2002 as base year:
2002 2005
Product p0 q0 p1 q1 p1q0 p0q0 p1q1 p0q1
I 60 50 70 40
II 50 20 40 40
III 30 30 30 40
Total A B C D E F
Find the price index for product II.
100
120
105
80
110
1 points
QUESTION 12
The probability of success on any trail of a binomial experiment is 25%. Find the probability that the proportion of successes in a sample of 1000 is less than 22%.
0.0284
0.02102
0.0143
0.0456
0.0325
1 points
QUESTION 13
Consider the following quantity index series: Shift the base year of this index series to 2007.
Year 2005 = 100
2005 100
2006 106
2007 116
2008 121
The new index for 2006 is:
110
105.31
91.38
88.68
1 points
QUESTION 14
Mr. Wilson is planning to buy himself a new car in 3.5 years’ time. He estimates that the car will cost him R138900 and that the trade-in on his old car 3.5 years from now will be R 15 500. Mr. Wilson decides to open a savings account in which he wants to deposit a fixed amount every month so that he will be able to afford the car. What amount should Mr. Wilson be saving monthly if the bank will pay interest of 13.7% per annum compounded monthly on the savings account?
R 2 307.03
R 2 596.81
R 77.28
None of the above
1 points
QUESTION 15
Suppose that the year is 2059. You remember that when you were a STK114 student back in the beginning of 2009, in the midst of a recession, you had a total of R 10 000 to invest amongst the following alternatives: Allan Gray, Stanlib and Investec. You invested half of your funds in Allan Gray and the remainder equally between the other two. At the end of 2059 all your investments together were worth R 500 000, with the following:
Investment House: Stanlib Allan Gray
Investment Value R 109 212.63 R 261 897.13
Looking back, which of the following is true:
A)You should have invested all your money in Investec, since this gave the best rate of return (8.2046%).
B)You should have invested all your funds in Allan Gray, since this gave an annual return over the period of 8.2389%.
C)You should have invested all your funds in Stanlib since this gave the best return over the period (8.2389%).
D)None of the above.
1 answer
1 answer