Statistics Examination
Guidelines
- One Word file should be used to submit the full assignment. If you make calculations in Excel and import the tables, be sure that the full table appears on the same page of your document.
- Your file should be named: SE1 Lastname Firstname
- Use the Harvard referencing system throughout the report.
- If you don't want to use an equation editor for formulas, please follow the simple approach below:
- Please use the pipe character | for conditional probability and not a forward slash (/).
- Please use the uppercase letter U for union.
- Please use the lowercase letter n for intersection
Part 1
Keywords: Descriptive Statistics, Frequency Histograms, Relative Frequency Histograms, Bar graph, Mean, Sample mean, Median, Mode, Range, Sample Variance, Sample standard deviation, Percentiles, Quartiles, z-score.
Exercise 1. For the following data set
|
14
|
12
|
23
|
11
|
9
|
3
|
|
12
|
3
|
7
|
19
|
8
|
6
|
|
3
|
19
|
16
|
5
|
3
|
8
|
|
13
|
5
|
4
|
13
|
2
|
1
|
|
4
|
7
|
18
|
17
|
4
|
9
|
|
8
|
7
|
11
|
10
|
11
|
12
|
Table 1: Data set Exercise
1. Construct a frequency histogram;
2. Construct a relative frequency histogram;
You are requested to solve the problem constructing frequency and relative frequency tables.
Exercise 2. The scores of 12 students randomly selected from MBALN-603 course are given:
80, 72, 65, 89, 36, 58, 71, 64, 49, 64, 76, 53
Compute mean, median mode, first and third quartiles.
Exercise 3. For the following data
| 32 |
31
|
27
|
35
|
| 21 |
25
|
28
|
26
|
| 30 |
32
|
26
|
29
|
| 27 |
23
|
31
|
29
|
Table 2: Data set Exercise 3
1. Compute mean, median, mode, first quartile, third quartile, range interquartile and range;
2. Compute the variance, standard deviation, coefficient variation, standard error of the mean and z-scores for each data point.
Part 2
Keywords: Tree diagram, Permutations, Combinations, Probability, Bayes' Rule
Exercise 4. Two boxes, A and B, contain red and green balls. Box A contains 7 red and 6 green balls and box B contains 8 red and 9 green balls. If the probability to choose box A is 55% find the probability:
1. to choose box B;
2. to choose a red ball from box A;
3. to choose a red ball;
4. to choose box A if the ball that has been chosen is red.
Exercise 5. A box contains 13 black and 11 white balls. Two balls are drawn from the box (without replacement) and it was noted the the second ball is black. Find the probability that the first ball is black.
Exercise 6. A box contains 7 red, 4 green, and 6 yellow balls.
1. If 4 balls are drawn at random without replacement, compute the probability that 2 are green, 1 is yellow and 1 is red.
2. If 4 balls are drawn at random with replacement, compute the probability that 2 are green, 1 is yellow and 1 is red.
Part 3
Keywords: Probability distributions, Random Variables, Discrete Probability Distributions, Continuous Random Variables, Binomial Distribution, The Normal Distribution, The Poisson Distribution
Exercise 7. Find the probability that in tossing a fair coin 9 times, there will appear:
1. 6 tails
2. 5 heads
3. at least 2 tails
4. not more than 3 heads
Exercise 8. The mean salary of 350 workers at company A is $1050 and the standard deviation is $150. If we assume that the salaries are normally distributed, compute the probability
1. a worker has salary more than $850
2. a worker has salary less than $900
3. a worker has salary between $800 and $1300
4. that exist exactly 102 workers with salary more than $900