Introduction to Statistical Quality Control
7th Edition
ISBN: 9781118146811
Author: Montgomery, Douglas C.
Publisher: John Wiley & Sons Inc
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Chapter 3, Problem 47E
Glass bottles are formed by pouring molten glass into a mold. The molten glass is prepared in a furnace lined with firebrick. As the firebrick wears, small pieces of brick are mixed into the molten glass and finally appear as defects (called “stones”) in the bottle. If we can assume that stones occur randomly at the rate of 0.00001 per bottle, what is the
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We consider the one-period model studied in class as an example. Namely, we assumethat the current stock price is S0 = 10. At time T, the stock has either moved up toSt = 12 (with probability p = 0.6) or down towards St = 8 (with probability 1−p = 0.4).We consider a call option on this stock with maturity T and strike price K = 10. Theinterest rate on the money market is zero.As in class, we assume that you, as a customer, are willing to buy the call option on100 shares of stock for $120. The investor, who sold you the option, can adopt one of thefollowing strategies: Strategy 1: (seen in class) Buy 50 shares of stock and borrow $380. Strategy 2: Buy 55 shares of stock and borrow $430. Strategy 3: Buy 60 shares of stock and borrow $480. Strategy 4: Buy 40 shares of stock and borrow $280.(a) For each of strategies 2-4, describe the value of the investor’s portfolio at time 0,and at time T for each possible movement of the stock.(b) For each of strategies 2-4, does the investor have…
Negate the following compound statement using De Morgans's laws.
Chapter 3 Solutions
Introduction to Statistical Quality Control
Ch. 3 - The content of liquid detergent bottles is being...Ch. 3 - The bore diameters of eight randomly selected...Ch. 3 - The service time in minutes from admit to...Ch. 3 - The Really Cool Clothing Company sells its...Ch. 3 - The nine measurements that follow are furnace...Ch. 3 - Consider the furnace temperature data in Exercise...Ch. 3 - Yield strengths of circular tubes with end caps...Ch. 3 - The time to failure in hours of an electronic...Ch. 3 - The data shown in Table 3E.2 are chemical process...Ch. 3 - An article in Quality Engineering (Vol. 4, 1992,...
Ch. 3 - Construct and interpret a normal probability plot...Ch. 3 - Construct and interpret a normal probability plot...Ch. 3 - Construct a normal probability plot of the failure...Ch. 3 - Construct a normal probability plot of the...Ch. 3 - Consider the viscosity data in Exercise 3.10....Ch. 3 - Table 3E.4 contains 20 observations on cycles to...Ch. 3 - An important quality characteristic of water is...Ch. 3 - Consider the outpatient service times in Exercise...Ch. 3 - Consider the call handling limes in Exercise 3.4....Ch. 3 - Consider the viscosity data in Exercise 3.10....Ch. 3 - Reconsider the yield data in Exercise 3.9....Ch. 3 - Consider the concentration of suspended solids...Ch. 3 - Consider the chemical process yield data in...Ch. 3 - Consider the chemical process yield data in...Ch. 3 - Construct a box plot for the data in Exercise 3.1.Ch. 3 - Construct a box plot for the data in Exercise 3.2.Ch. 3 - Suppose that two fair dice are tossed and the...Ch. 3 - Find the mean and variance of the random variable...Ch. 3 - A mechatronic assembly is subjected to a final...Ch. 3 - The probability distribution of x is f(x) = kex, 0...Ch. 3 - The random variable x takes on the values 1, 2, or...Ch. 3 - The probability distribution of the discrete...Ch. 3 - A manufacturer of electronic calculators offers a...Ch. 3 - The net contents in ounces of canned soup is a...Ch. 3 - A production process operates with 1 %...Ch. 3 - Continuation of Exercise 3.35. Consider the...Ch. 3 - A random sample of 50 units is drawn from a...Ch. 3 - A sample of 100 units is selected from a...Ch. 3 - Suppose that 10% of the adult population has blood...Ch. 3 - Patients arriving at an outpatient clinic are...Ch. 3 - A stock brokerage has four computers that are used...Ch. 3 - A computer system uses passwords consisting of the...Ch. 3 - An electronic component for a medical X-ray unit...Ch. 3 - A lot of size N = 30 contains three nonconforming...Ch. 3 - A textbook has 500 pages on which typographical...Ch. 3 - Surface-finish defects in a small electric...Ch. 3 - Glass bottles are formed by pouring molten glass...Ch. 3 - The billing department of a major credit card...Ch. 3 - A production process operates in one of two...Ch. 3 - An inspector is looking for nonconforming welds in...Ch. 3 - The tensile strength of a metal part is normally...Ch. 3 - The output voltage of a power supply is normally...Ch. 3 - Continuation of Exercise 3.52. Reconsider the...Ch. 3 - If x is normally distributed with mean and...Ch. 3 - The life of an automotive battery is normally...Ch. 3 - A lightbulb has a normally distributed light...Ch. 3 - Derive the mean and variance of the binomial...Ch. 3 - Derive the mean and variance of the Poisson...Ch. 3 - Derive the mean and variance of the exponential...Ch. 3 - Derive the mean and variance of the geometric...
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- Negate the following compound statement using De Morgans's laws.arrow_forwardQuestion 6: Negate the following compound statements, using De Morgan's laws. A) If Alberta was under water entirely then there should be no fossil of mammals.arrow_forwardNegate the following compound statement using De Morgans's laws.arrow_forward
- Characterize (with proof) all connected graphs that contain no even cycles in terms oftheir blocks.arrow_forwardLet G be a connected graph that does not have P4 or C3 as an induced subgraph (i.e.,G is P4, C3 free). Prove that G is a complete bipartite grapharrow_forwardProve sufficiency of the condition for a graph to be bipartite that is, prove that if G hasno odd cycles then G is bipartite as follows:Assume that the statement is false and that G is an edge minimal counterexample. That is, Gsatisfies the conditions and is not bipartite but G − e is bipartite for any edge e. (Note thatthis is essentially induction, just using different terminology.) What does minimality say aboutconnectivity of G? Can G − e be disconnected? Explain why if there is an edge between twovertices in the same part of a bipartition of G − e then there is an odd cyclearrow_forward
- Let G be a connected graph that does not have P4 or C4 as an induced subgraph (i.e.,G is P4, C4 free). Prove that G has a vertex adjacent to all othersarrow_forwardWe consider a one-period market with the following properties: the current stock priceis S0 = 4. At time T = 1 year, the stock has either moved up to S1 = 8 (with probability0.7) or down towards S1 = 2 (with probability 0.3). We consider a call option on thisstock with maturity T = 1 and strike price K = 5. The interest rate on the money marketis 25% yearly.(a) Find the replicating portfolio (φ, ψ) corresponding to this call option.(b) Find the risk-neutral (no-arbitrage) price of this call option.(c) We now consider a put option with maturity T = 1 and strike price K = 3 onthe same market. Find the risk-neutral price of this put option. Reminder: A putoption gives you the right to sell the stock for the strike price K.1(d) An investor with initial capital X0 = 0 wants to invest on this market. He buysα shares of the stock (or sells them if α is negative) and buys β call options (orsells them is β is negative). He invests the cash balance on the money market (orborrows if the amount is…arrow_forwardDetermine if the two statements are equivalent using a truth tablearrow_forward
- Question 4: Determine if pair of statements A and B are equivalent or not, using truth table. A. (~qp)^~q в. р л~9arrow_forwardDetermine if the two statements are equalivalent using a truth tablearrow_forwardQuestion 3: p and q represent the following simple statements. p: Calgary is the capital of Alberta. A) Determine the value of each simple statement p and q. B) Then, without truth table, determine the va q: Alberta is a province of Canada. for each following compound statement below. pvq р^~q ~рл~q ~q→ p ~P~q Pq b~ (d~ ← b~) d~ (b~ v d) 0 4arrow_forward
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