2. Each morning, the manager of a bakery has to decide how many cakes they shouldbake for sale that day. The manager knows that on any given day, the demand forcake is a random variable taking the values 0, 1, 2, 3, 4, 5, 6 and 7, each with probability1/8. He also knows that he will make a profit of $2 for each cake that he sells, and aloss of $0.75 for each cake he bakes but doesn't sell. Find the expected profit for theday if he chooses to bake(a) one cake;(b) two cakes;(c) three cakes;(d) four cakes;(e) five cakes;(f) six cakes;(g) seven cakes.How many cakes should he choose to make in order to maximize his expected profit?Hint: If the demand for cake exceeds to the number of cakes baked, how many cakesare sold?

The random variable X indicates the demand for a cake. It takes values 0, 1, 2, 3, 4, 5, 6 and 7,…

Answered: 2. Each morning, the manager of a…

A First Course in Probability (10th Edition)

10th Edition

ISBN:9780134753119

Author:Sheldon Ross

Publisher:Sheldon Ross

Chapter1: Combinatorial Analysis

Section: Chapter Questions

Problem 1.1P: a. How many different 7-place license plates are possible if the first 2 places are for letters and...

See similar textbooks

Similar questions

A study tracked a large group of people for 10 years. At the start of the study, 20% were heavy smokers (H), 30% were light smokers (L), and 50% were non-smokers (N). The interest of the study was whether the people in the study died during the study (D) or not die (Dc ). The probability that a light smoker died during the study was twice that of the probability of a non-smoker dying. Also, the probability that light smoker died during the study was half that of the probability of a heavy smoker dying. A randomly selected person from the study died during the study. What is the probability that this person was a heavy smoker (given they died, what is the probability they were a heavy smoker H)?
A medical researcher is studying the spread of a virus in a population of 1000 laboratory mice. During any week, there is an 80% probability that an infected mouse will overcome the virus, and during the same week there is a 10% probability that a noninfected mouse will become infected. Three hundred mice are currently infected with the virus. How many will be infected (a) next week and (b) in 3 weeks?
In a population of 10,000, there are 5000 nonsmokers, 2500 smokers of one pack or less per day, and 2500 smokers of more than one pack per day. During any month, there is a 5% probability that a nonsmoker will begin smoking a pack or less per day, and a 4% probability that a nonsmoker will begin smoking more than a pack per day. For smokers who smoke a pack or less per day, there is a 10% probability of quitting and a 10% probability of increasing to more than a pack per day. For smokers who smoke more than a pack per day, there is a 9% probability of quitting and a 10% probability of dropping to a pack or less per day. How many people will be in each group in 1 month, in 2 months, and in 1 year? (Round your answers to the nearest whole number.)(a) in 1 month:nonsmokers:1 pack/day or less:more than 1 pack/day:(b) in 2 months:nonsmokers:1 pack/day or less:more than 1 pack/day:(c) in 1 year:nonsmokers:1 pack/day or less:more than 1 pack/day:
At a local college, four sections of economics are taught during the day and two sections are taught at night. 70 percent of the day sections are taught by full-time faculty. 10 percent of the evening sections are taught by full-time faculty. If Jane has a part-time teacher for her economics course, what is the probability that she is taking a night class?
The Business School at State University currently has three parking lots, each containing 155 spaces. Two hundred faculty members have been assigned to each lot. On a peak day, an average of 70% of all lot 1 parking sticker holders show up, an average of 72% of all lot 2 parking sticker holders show up, and an average of 74% of all lot 3 parking sticker holders show up. a. Given the current situation, estimate the probability that on a peak day, at least one faculty member with a sticker will be unable to find a spot. Assume that the number who show up at each lot is independent of the number who show up at the other two lots. Compare two situations: (1) each person can park only in the lot assigned to him or her, and (2) each person can park in any of the lots (pooling). (Hint: Use the RISKBINOMIAL function.) If needed, round your answer to a whole percentage and if your answer is zero, enter "0". No pooling: Pooling: 51.4 % 83.8 % b. Now suppose the numbers of people who show up at…
Your assembly plant buys identical widgets from 3 suppliers, A, B, and C. Suppliers A and B each supplies a quarter of your widgets each day, whereas Supplier C supplies the remaining 50%. Of the widgets supplied by A, B, and C, the average numbers of defective widgets are 5%, 3%, and 7%, respectively.(a) If a widget is selected at random, what is the probability of it being defective? Let A, B, C be the event of a randomly picked widget being sourced by suppliers A, B, and C, respectively. Furthermore, let D be the event of a randomly-picked widget being defective. Use these symbols A, B, C, and D when you do this problem.(b) What is the probability of a randomly-picked widget being supplied by A and also being defective?(c) If a randomly-picked widget is defective, what’s the probability of it having been supplied by A?(d) If a randomly-picked widget is defective, what’s the probability of it having been supplied by B? By C? What's the sum of the 3 probabilities…
Becky and Carla take an advanced yoga class. Becky can hold 29% of her poses for over a minute, while Carla can hold 35% of her poses for over a minute. Suppose each yoga student is asked to hold 50 poses. Let B the proportion of poses Becky can hold for over a minute and C = the proportion of poses Carla can hold for over a minute. What is the probability that Becky's proportion of poses held for over a minute is greater than Carla's? Find the z-table here. O 0.159 O 0,259 0 0.448 O 0,741 Save and Exit Next Submit Math and rem 96 & 7 8 9. 10
Brian is in charge of the mailroom of the Boryk Corporation. Each day the company receives several packages via the U.S. Postal system, for which he must sign. The following is the probability distribution for the number of daily pieces of mail that comes via the Postal system.
Suppose the amount of gasoline sold daily at a service station is uniformly distributed with a minimum of 1571 gallons and a maximum of 8154 gallons. What is the probability that daily sales will fall between 1951 gallons and 4845 gallons?
In the last week of the semester, Stéphane decides to “reward” the students by no longer limiting himself to 4 exercises and instead assigning every activity he writes. If a student with a 60% chance of correctly answering an exercise is expected to answer three correctly, what is the probability that Stéphane did not have a visitor that week?
In small-town, there are three different types of weather conditions: a sunny day, rainy day, and windy day. A sunny day never happens two days in a row. If it is a sunny day, it is as likely to have a rainy day or windy day the next day. If it is a windy day or rainy day, it has an even chance of having the same conditions the next day. For the other 50%, it is two times more likely to have a bad weather condition than a sunny day. Draw a transition diagram. Is it an ergodic Markov chain (support your answer)? Obtain a transition probability matrix. What is the probability of having a sunny day 2 days from now, if today is a rainy day (Calculate without using matrix multiplication, hint: calculate just the needed value or matrix element)? What is the probability of having sunny 4 days from now, if today is a rainy day? What is the probability of having a rainy day 3 days from now if today is a windy day? Obtain the mean first passage time for all states.
In a certain population of caribou, the probability of an animal’s being sickly 1/20. If a caribou is sickly, the probability of its being eaten by wolves is ⅓. If a caribou is not sickly, the probability of its being eaten by wolves is 1/150. If a caribou is chosen at random from the herd, what is the probability of the event that it will be eaten by wolves.

SEE MORE QUESTIONS

Recommended textbooks for you

A First Course in Probability (10th Edition)

Probability

ISBN:

9780134753119

Author:

Sheldon Ross

Publisher:

PEARSON

A First Course in Probability

Probability

ISBN:

9780321794772

Author:

Sheldon Ross

Publisher:

PEARSON

A First Course in Probability (10th Edition)

Probability

ISBN:

9780134753119

Author:

Sheldon Ross

Publisher:

PEARSON

A First Course in Probability

Probability

ISBN:

9780321794772

Author:

Sheldon Ross

Publisher:

PEARSON

SEE MORE TEXTBOOKS