Pakistan International School Riyadh
Class XII
1. How many possible permutations can be formed from the word ‘statistics’? 2. In how many ways can a team of 11 players be chosen from a total of 16 players? 3. State multiplicative theorem of probability for dependent events. 4. An aptitude test with 4 options. If a student marks the options of the questions randomly and independently, then find the probability of being correct to 4 questions. 5. A can solve 75% questions in a book and B can solve 60% questions in that book. Find the probability that randomly selected questions is solved by them? 6. What is the probability of getting at least 2 heads when 3 coins are tossed? 7. Find P(A ∩ B) if P(A) = ¼ and P(B) = 1/3 and p(A U B) = ½ . 8. State the laws of expectation.

9. Describe the properties of discrete probability distribution. 10. Given E(X) = 0.55, Var(X) = 1.55 and Y = 2X + 1. Find E(Y) and Var(Y). 11. Show that the mean of the binomial distribution (q + p)2 is 2p. 12. Show that mean is 2p and σ2 = 2pq for a binomial distribution in which n = 2. 13. A random variable X has a binomial distribution with E(X) = 2.4 and p = 0.3. Find the standard deviation of X. 14. Describe the normal distribution and write down its equation. 15. What is standard normal variable?

16. The value 2nd moment about mean in a normal distribution is 5. Find the 3rd and 4th moment about mean for this distribution. 17. Is every symmetrical distribution a normal distribution? 18. What is the relation between the binomial and normal distribution? 19. Define sampling units and frame.

20. What is the difference between sampling and non-sampling error? 21. Name the four techniques used in probability sampling. 22. Given P1 = 2/3, n1 = 2, P2 = 2, n2 = 2. Find µP1-P2 and σP1 – P2. 23. What is the difference between sampling with replacement and without replacement? 24. Find 90% confidence interval of µ from a sample...

...QUESTION 21
The finishing process on new furniture leaves slight blemishes. The table below displays a manager's probability assessment of the number of blemishes on one piece of new furniture.
Number of Blemishes
0
1
2
3
4
5
Probability
0.34
0.25
0.19
0.11
0.07
0.04
1. On average, how many blemishes do we expect on one piece of new furniture?
2. What is the variance of blemishes on one piece of new furniture? (round to the nearest hundredth) ...

...Practice Problems 1-KEY 1. The closing stock price of Ahmadi, Inc. for a sample of 10 trading days is shown below. Day Stock Price 1 84 2 87 3 84 4 88 5 85 6 90 7 91 8 83 9 82 10 86
For the above sample, compute the following measures. a. b. c. The mean = ∑X/n = 860/10 = 86 The median = (85+86)/2 = 85.5 The variance = ∑ X - X 2/ n-1 = {(84-86)2 + (87-86)2 + (84-86)2 + (88-86)2 + (85-86)2 + (90-86)2 + (91-86)2 + (83The standard deviation = √8.89 = 2.98 The coefficient of variation = 2.98/86...

...|4 |
|Pensylvania |6 |3 |4 |
Ho: Account balances are independent of branch.
H1: Account balances are independent of branch
Test Statistic:
Chi square is given by (Oi – Ei)^2 / Ei ~ χ2 with 2*3= 6 degrees of freedom
The calculated value of chi-square is 11.89625
Critical value for 5% level of significance is 12.5916
Since the calculated value is...

...1. Introduction
This report is about the case study of PAR, INC. From the following book: Statistics for Business an Economics, 8th edition by D.R. Anderson, D.J. Sweeney and Th.A. Williams, publisher: Dave Shaut. The case is described at page 416, chapter 10.
2. Problem statement
Par, Inc. has produced a new type of golf ball. The company wants to know if this new type of golf ball is comparable to the old ones. Therefore they did a test, which consists out of 40...

...1. A radio station that plays classical music has a “By Request” program each Saturday night. The percentage of requests for composers on a particular night are listed below:
Composers Percentage of Requests
Bach 5
Beethoven 26
Brahms 9
Dvorak 2
Mendelssohn 3
Mozart 21
Schubert 12
Schumann 7
Tchaikovsky 14
Wagner 1
a. Does the data listed above comprise a valid probability distribution?...

...shorter than TT Air, it does not significantly affect the output as the one day does not change much (unless there had been a market shock). However based on Central Limit Theorem, if the sample size is greater than or equal to 30 samples, the sample statistics reflect the time population parameters.
• The Median data does not show much in this case as the range (4.7 AA Fly and 6.8 TT Air) is small for both AA Fly and TT Air. This means that the mean is more applicable to be...