# Quantitative Analysis for Managerial Applications

**Topics:**Chi-square distribution, Dice, Statistical tests

**Pages:**5 (1330 words)

**Published:**April 23, 2013

Course Code:MS 08

Course Title:Quantitative Analysis for Managerial Applications Assignment No.:MS-08/TMA/SEM-I/2013

Coverage:All Blocks

Note : Attempt all the questions and submit this assignment on or before 30th April, 2013 to the coordinator of your study center.

1.A sum of `8550 is to be paid in 15 installments where each installment is `10 more than the previous installment. Find the first installment and the last installment.

Let x = the first payment.

The sequence of 15 payments is

(1) x, x+10, x+20, x+30, ... , x+140

The sum of these 15 payments is

(2) 15x + 10*(14*15/2) or

(3) 15x + 1050

Now set (3) equal to the total sum to be made and get

(4) 15x + 1050 = 8550 or

(5) 15x = 7500 or

(6) x = 500

The last payment in (1) is x + 140 or

(7) 15th = 640

Answer: The first payment is $500 and the last payment is $640. I'll leave it to you to add up the sequence of (1) to "prove" that our answer is right. LOL

2.A salesman is known to sell a product in 3 out of 5 attempts. While another salesman in 2 out of 5 attempts. Find the probability that a.No sales will happen

b.Either of them will succeed in selling the product

Let A be the event that the first salesman will sell the product and B be the event that the second salesman will sell the product. Given

(1) Probability that no sales will happen = P(A') × P(B')

(2) Probability that either of the salesman will succeed in selling the product = P(A') × P(B) + P(A) × P(B')

3.A hundred squash balls are tested by dropping from a height of 100 inches and measuring the height of the bounce. A ball is “fast” if it rises above 32 inches. The average height of bounce was 30 inches and the standard deviation was ¾ inches. What is the chance of getting a “fast” standard ball?

T otal no. of observations N = 100

Mean,μ = 30inches

Standard deviation, σ=3/4 inches=0.75 inches

Suppose 'x' is the normal variable=32 inches

4.Explain the chi-square testing- (i) as a test for independence of attributes, and (ii) as a test for goodness of fit.

About the Chi-Square Test

Generally speaking, the chi-square test is a statistical test used to examine differences with categorical variables. There are a number of features of the social world we characterize through categorical variables - religion, political preference, etc. To examine hypotheses using such variables, use the chi-square test. The chi-square test is used in two similar but distinct circumstances: a.for estimating how closely an observed distribution matches an expected distribution - we'll refer to this as the goodness-of-fit test b.for estimating whether two random variables are independent. The Goodness-of-Fit Test

One of the more interesting goodness-of-fit applications of the chi-square test is to examine issues of fairness and cheating in games of chance, such as cards, dice, and roulette. Since such games usually involve wagering, there is significant incentive for people to try to rig the games and allegations of missing cards, "loaded" dice, and "sticky" roulette wheels are all too common. So how can the goodness-of-fit test be used to examine cheating in gambling? It is easier to describe the process through an example. Take the example of dice. Most dice used in wagering have six sides, with each side having a value of one, two, three, four, five, or six. If the die being used is fair, then the chance of any particular number coming up is the same: 1 in 6. However, if the die is loaded, then certain numbers will have a greater likelihood of appearing, while others will have a lower likelihood. One night at the Tunisian Nights Casino, renowned gambler Jeremy Turner (a.k.a. The Missouri Master) is having a fantastic night at the craps table. In two hours of playing, he's racked up $30,000 in winnings and is showing no sign of stopping. Crowds are gathering around him to watch his streak - and The Missouri Master is telling...

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