Suppose that a grocery store purchases 4 cartons of skim milk at the wholesale price of $1.00 per carton and retails the milk at $1.50 per carton. After the expiration date, the unsold milk is removed from the shelf and the grocer receives a credit from the distributor equal to three-fourths of the wholesale price. The grocer is not penalized for any product shortage. Given the probability distribution of the random variable X, the number of cartons that are sold from this lot is as follows: 2 3 4 f(x) 1/15 2/15 2/15 3/15 4/15 3/15 Construct the cumulative distribution function of f(x) b. How many cartons are expected to be sold? a. What is the expected profit of the grocer? d. Calculate for the standard deviation of the grocer's profits. C.

Suppose that a grocery store purchases 4 cartons of skim milk at the wholesale price of $1.00 per carton and retails the milk at $1.50 per carton. After the expiration date, the unsold milk is removed from the shelf and the grocer receives a credit from the distributor equal to three-fourths of the wholesale price. The grocer is not penalized for any product shortage. Given the probability distribution of the random variable X, the number of cartons that are sold from this lot is as follows: 2 3 4 f(x) 1/15 2/15 2/15 3/15 4/15 3/15 Construct the cumulative distribution function of f(x) b. How many cartons are expected to be sold? a. What is the expected profit of the grocer? d. Calculate for the standard deviation of the grocer's profits. C.

MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

Section: Chapter Questions

Problem 1P

See similar textbooks

Related questions

Q: 35 year old man pays $191 for a one year life insurance policy with a coverage of $140,000 if the…

A: Given that a 35 year old man pays $191 for a one year life insurance policy with a coverage of…

Q: Find an equation of the line with the given slope that passes through the given point. Write the…

A: Here, slope =2, the line passes through the point (3,3).

Q: rawer contains 20 writing utensils: 6 red pens, 3 black pens, 4 blue pens, and 7 pencils. Professor…

Q: In a new card game, you start with a well-shuffled full deck and draw 3 cards without replacement.…

A: The objective of this question is to create a probability model for a card game, calculate the…

Q: The Law of large numbers states that as the number of repetitions of an experiment n increases, the…

A: The law of large numbers is one of the important principles of probability. It states that as the…

Q: the company figures that the probability of the house being burned down by fire is 0.005, what will…

A: Given that an insurance company insures a house worth P4,500,000 for an annual premium of P25,000.

Q: a certain company, there are weekly inspections done by an outsourced audit team. They find one out…

A: Given data,They find one out of eight hundred defective products every week probability of defective…

Q: Assume that the store stocks 30 percent brand A, 50 percent brand B, and the rest are brand X.…

A: According to the given information:The store stocks 30% brand A in which 15% does not provide the…

Q: What is the probability function for X? What is the expected value of your winnings? If the…

A: 1.

Q: You live in an area that has a possibility of incurring a massive earthquake, so you are considering…

A: To apply Bayes' decision rule, we need to compare the expected assets after one year for two…

Q: A man wishes to purchase a life insurance policy that will pay the beneficiary $25,000 in the event…

A: It is given that he will live another year is 0.92 and the amount of gain is 25,000.

Q: According to survival probability tables, the probability that an 80 year old male living 1…

A: The probability that an 80 year old male living 1 additional year is 0.93, then the probability that…

Q: A box contains 20 electric lamps of which 5 are defective. A man selects two lamps randomly and he…

Q: You have 4 pennies (1¢ each) and 3 nickels (5¢ each) in your pocket. You reach in and blindly grab…

Q: An insurance policy on an electrical device pays a benefit of $4800 if the device fails during the…

Q: In looking over customer data for your local ice cream shop, you estimate the following…

A: The given probabilities are as follows:P(vanilla)=0.5P(sundae)=0.5P(vanilla AND sundae)=0.2

Q: When the health department tested private wells in a county for two impurities commonly found in…

A: Solution: Given information: Let A be the event that the wells has impurity A B: be the event that…

Q: The normal rate of infection of a certain disease with the children is found to be 20%. In an…

Q: Brandybuck Insurance Company (BIC) is deciding whether to insure the lives of those leading a quest…

A: Given: BIC charges a premium = 6591 silver coins. BIC pay a death benefit = 47460 The probability of…

Q: Suppose a life insurance company sells a $120,000 one-year term life insurance policy to a…

A: Given P=0.999356 q=1-p =1-0.999356 =0.000644

Q: Assume that the store stocks 40 percent brand A, 40 percent brand B, and the rest are brand X.…

A: Brand X is (100-40-40)=20% P(A)=0.40 , P(B)= 0.40 , P(X)= 0.20 Let, C= event that the number of…

Q: Assume that the store stocks 30 percent brand A, 50 percent brand B, and the rest are brand X.…

A: Let A be the event of choosing stock A , B be the event of choosing stock B , X be the event of…

Q: Suppose that a box contains 8 marbles: 2 blue and 6 green. Two marbles are drawn without…

A: From the provided information,Box contains 8 marbles.2 are blue and 6 are green.Two marbles are…

Q: those who were known to have the disease showed a positive test result for the disease. Of those who…

Q: At a lottery competition, a person pays 20R to participate in the competition. If he rolls two dice…

A: Expected gain = sum(p*x)

Q: Brandybuck Insurance Company (BIC) is deciding whether to insure the lives of those leading a quest…

A: From the given information, the probability of surviving such a quest is 94.0% and the probability…

Q: Avicenna, a major insurance company, offers five-year life insurance policies to 65-year-olds. If…

Q: A sociologist hypothesizes that the expected proportion of the number of children in certain family…

A: Null Hypothesis: H0: All expected proportion of the number of children in certain family units…

Q: A manufacturer of car crankshafts is attempting to determine the likelihood of faulty samples in a…

A: Since there are only two types of samples - good and defective - and we are drawing two samples,…

Q: A company produces 10,000 plastic papers per day. This company supplies papers to a shops which…

A: Let X as the random variable of interest here, which is the number of packages of defective papers.…

Q: The research department of a commercial bank estimates that the 5% of its loans will go into…

A: Given: Proportion of default loans estimated by research department (θ) = 0.05 Number of customers…

Concept explainers

Compound Probability

Compound probability can be defined as the probability of the two events which are independent. It can be defined as the multiplication of the probability of two events that are not dependent.

Tree diagram

Probability theory is a branch of mathematics that deals with the subject of probability. Although there are many different concepts of probability, probability theory expresses the definition mathematically through a series of axioms. Usually, these axioms express probability in terms of a probability space, which assigns a measure with values ranging from 0 to 1 to a set of outcomes known as the sample space. An event is a subset of these outcomes that is described.

Conditional Probability

By definition, the term probability is expressed as a part of mathematics where the chance of an event that may either occur or not is evaluated and expressed in numerical terms. The range of the value within which probability can be expressed is between 0 and 1. The higher the chance of an event occurring, the closer is its value to be 1. If the probability of an event is 1, it means that the event will happen under all considered circumstances. Similarly, if the probability is exactly 0, then no matter the situation, the event will never occur.

Question

3. Suppose that a grocery store purchases 4 cartons of skim milk at the wholesale price of $1.00 per carton
and retails the milk at $1.50 per carton. After the expiration date, the unsold milk is removed from the
shelf and the grocer receives a credit from the distributor equal to three-fourths of the wholesale price.
The grocer is not penalized for any product shortage. Given the probability distribution of the random
variable X, the number of cartons that are sold from this lot is as follows:
X
1
2
3
4
5
f(x) 1/15 2/15 2/15 3/15 4/15 3/15
Construct the cumulative distribution function of f(x)
b. How many cartons are expected to be sold?
c. What is the expected profit of the grocer?
d. Calculate for the standard deviation of the grocer's profits.
a.

Expert Solution

This question has been solved!

Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.

This is a popular solution!

SEE SOLUTION Check out a sample Q&A here

Step 1

Step 2

Step 3

Step 4

Trending now

This is a popular solution!

Step by step

Solved in 4 steps

SEE SOLUTION Check out a sample Q&A here

Knowledge Booster

$Conditional Probability, Decision Trees, and Bayes' Theorem$

Learn more about

Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, statistics and related others by exploring similar questions and additional content below.

Similar questions

A believer in the "random walk" theory of stock markets thinks the value of an index of stock prices has a 0.6 probability of rising in any year. The change in the value of the index in any given year is not affected by whether it rose or fell in earlier years. You plan to record the value for the index in each of the next eight years. Let the random variable, X, represent the number of years (out of the next 8 years) in which the value of the index rises. a) If X is distributed according to the binomial probability distribution, what are the values for n and p?o b) What are the possible values X can take, or equal? QMETH 201, Homework 3 c) Calculate the probability X = 30 d) Calculate the expected value for X. e) Calculate the standard deviation for X. 4
When the health department tested private wells in a county for two impurities commonly found in drinking water, it found that 10% of the wells had neither impurity, 90% had impurity A, and 20% had impurity B. (Obviously, some had both impurities.) If a well is randomly chosen from those in the county, find the probability distribution for Y, the number of impurities found in the well. P(no impurities)= P(exactly one impurity)= P(both impurities)=
A firm plans to bid $. 300 per kg. For a contract to supply 1,000 kg. Of a metal. It has two competitors A and B and it assumes that the probability that A will bid less than $. 300 per kg. Is 0.3 and that B will bid less than $ 300 per kg. Is 0.7. If the lowest bidder gets all the business and the firms bid independently, what is the expected value of the contract to the firm?
For 10 percent of the products in a category, a firm fails to satisfy all demand during themonth. What is its in-stock probability?
The percentage of people in the population who have a certain disease is 22%. There is a test for the disease that is fairly accurate. Of the people who have the disease who take the test, it reports that 6% of them do not have the disease. Of the people who do not have the disease who take the test, it reports that 6% of them have the disease. Suppose that a person takes the test and it reports that they have the disease. Compute the probability that the person does not have the disease. Round your answer to two decimal places. (If necessary, consult a list of formulas.) 0 X Ś
A small business is studying the number of customers that enter the store. They record the number of customers entering every hour for three days, and find that 27% of the time two customers enter the store in an hour, 28% of the time of the time one customer enters the store in an hour, and the remainder of the time no one enters the store in an hour. What is the expected number of customers per hour?
Brandybuck Insurance Company (BIC) is deciding whether to insure the lives of those leading a quest to Moria. Based on past experience, the probability of surviving such a quest is 88.9%. If BIC charges a premium of 8,240 silver coins and would pay a death benefit of 56,881 silver coins if the insured were to die, what is the expected value of this insurance policy to BIC? Round to the nearest silver coin as needed. If the expected value is a loss to BIC, enter your answer as a negative number. Phil Dunphy, a real estate agent, is considering whether he should list an unusual $303,402 house for sale. If he lists it, he will need to spend $3,848 in advertising, staging, and fresh cookies. The current owner has given Phil 6 months to sell the house. If he sells it, he will receive a commission of $23,557. If he is unable to sell the house, he will lose the listing and his expenses. Phil estimates the probability of selling this house in 6 months to be 73%. What is the expected…
An insurance company estimates the probability of an earthquake in the next year to be 0.0013. The average damage done by an earthquake is estimated to be $60,000. If the company offers earthquake insurance for $100, what is their expected value of the policy?
Willow Brook National Bank operates a drive-up teller window that allows customers to complete bank transactions without getting out of their cars. On weekday mornings, arrivals to the drive-up teller window occur at random, with an arrival rate of 30 customers per hour or 0.5 customers per minute. Let's assume that the service times for the drive-up teller follow an exponential probability distribution with a service rate of 45 customers per hour, or 0.75 customers per minute. Determine the following operating characteristics for the system. (Round your answers to four decimal places.) (a) The probability that no customers are in the system 1353 (b) The average number of customers waiting 1786 (c) The average number of customers in the system 1.25 (d) The average time (in min) a customer spends waiting 4.2 X min (e) The average time (in min) a customer spends in the system x min 1 (f) The probability that arriving customers will have to wait for service 73 X
Brandybuck Insurance Company (BIC) is deciding whether to insure the lives of those leading a quest to Moria. Based on past experience, the probability of surviving such a quest is 95.5%. If BIC charges a premium of 9,900 silver coins and would pay a death benefit of 49,518 silver coins if the insured were to die, what is the expected value of this insurance policy to BIC? Round to the nearest silver coin as needed. If the expected value is a loss to BIC, enter your answer as a negative number.
Each day, John's mother gives him money before he goes to school: 50% of the time he gets $5, 35% of the time he gets $10 and the rest of the time he gets $20. Determine the expectation and variance for how much money John gets each day. For the next 100 school days, John plans to save all the money his mother gives him. What is the approximate probability he is able to save more than $1000? Assume independence. If he realizes he has to spend an average of $4 a day with a standard deviation of $0.75, what is the approximate probability that he saves less than $400? Assume independence.