Essay on Arithmetic Mean and Confidence Interval

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THE UNIVERSITY OF THE FREE STATE
DEPARTMENT OF MATHEMATICAL STATISTICS AND ACTUARIAL SCIENCE
BUSINESS CALCULATIONS AND STATISTICS –
BCS 524; STK 124 – TEST 1: 27 AUGUST 2012
TOTAL: 60 Time: 2 hours

TASK NUMBER: 01
SECTION A
Instructions:
 Answer the following 18 multiple-choice questions on the optical form provided.
 There is only one correct answer to every question.
 Choose the best possible answer.
 Round off ONLY your final answer.
 Use a DARK PENCIL to complete the optical form.
 Pages for rough work are attached at the end of the question paper.
 Ensure that you fill in the correct TASK NUMBER on the optical form.
 If your surname, initials, student number and task number is not completed correctly, 10% will be deducted from your final mark

Consider the information in the following table before answering questions 1 – 3 below.
The probability to win for a Team A, which plays 5 matches per month is as follows, where P(1) is three times more likely to occur as P(5).

X 0 1 2 3 4 5
P(x) 0.04 ? 0.16 0.37 0.15 ?

1. Calculate the probability that Team A will win more than 3 games per month.
a) 0.28 b) 0.52 c) 0.22
d) 0.07 e) 0.15 f) None of the above

2. Calculate the expected value of winning for Team A.
a) 2.66 b) 0.72 c) 2.59
d) 3.5 e) 2.682 f) None of the above

3. Calculate the standard deviation of winning for Team A.
a) 2.59 b) 1.6219 c) 1.3244
d) 1.1354 e) 1.1508 f) None of the above

4. If a person receives an A in Intermediate Algebra, the probability of that person getting an A for statistics is 0.4. If 4 people pass Algebra with an A, what is the expected value that they will get an A in Statistics?
a) 1.6 b) 10 c) 2.4
d) 0.4 e) 0.96 f) 0.9798

5. If a person receives an A in Intermediate Algebra, the probability of that person getting an A for statistics is 0.4. If 4 people pass Algebra with an A, calculate the standard deviation that they will get an A in Statistics.
a) 0.96 b) 0.9798 c) 2.4
d) 1.1649 e) 3.1623 f) 1.5492

6. If a person receives an A in Intermediate Algebra, the probability of that person getting an A for statistics is 0.4. If 4 people pass Algebra with an A, find the probability that exactly 2 will get an A in Statistics.
a) 8 b) 0.3456 c) 0.6544
d) 0.8 e)0.8208 f) 0.1792

7. The probability of students graduating from university in four years is 0.55. If 7 students are selected at random, find the probability that at least 2 of them will not graduate in four years.
a) 0.3923 b) 0.6077 c) 0.0357
d) 0.9643 e) 0.8976 f) 0.1024

8. The probability of students graduating from university in four years is 0.55. If 7 students are selected at random, find the probability that at most 2 of them will graduate in four years.
a) 0.1173 b) 0.2140 c) 0.1529
d) 0.8471 e) 0.0357 f) 0.9643

Consider the information in the following table before answering questions 9 – 11.
Many manufacturing problems involve the accurate matching parts such as shafts that fit into a valve hole. A particular design requires a shaft with a diameter 22.0 mm, but shaft with diameters between 21.90 mm and 22.010 mm are acceptable. Suppose that the manufacturing process yields shafts with diameters normally distributed with a mean of 22.002 mm and a standard deviation of 0.05 mm

9. What is the probability of shafts with diameter more than 21.90 mm?
a) 0.1020 b) 0.9793 c) 0.0207
d) 0.3228 e) 0.8980 f) 0.6772

10. As If 1500 manufacturing processes were observed, how many will have a shaft with diameter less than 22.15 mm
a) 0.0015 b) 1 498 c) 1 495
d) 1 497 e) 1 502 f) 0.9985

11. Suppose that a random sample of 36 manufacturing processes are taken, what is the probability that their shafts will have an average diameter less than 22 mm
a) 0.5160 b) 0.0749 c) 0.9251
d) 0.4052 e) 0.4840 f) 0.5948

12. If all possible
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