1 (a) A pair of dice is rolled, and the number that appears uppermost on each die is observed. Refer to this experiment and find the probability of the given event. (Enter your answer as a fraction.)
The sum of the numbers is either 7 or 11.
(b) An experiment consists of selecting a card at random from a 52-card deck. Refer to this experiment and find the probability of the event. (Enter your answer as a fraction.)
A face card (i.e., a jack, queen, or king) is drawn.
(c) An experiment consists of selecting a card at random from a 52-card deck. Refer to this experiment and find the probability of the event. (Enter your answer as a fraction.)
A black face card is not drawn.
In: Statistics and Probability
A psychology experiment on memory was conducted which required participants to note which songs they found pleasing. Based on many results, the (partial) probability distribution below was determined for the discrete random variable X = number of songs found pleasing (during a fixed time period).
| X = # songs | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 |
| Probability | 0 | 0.02 | 0.04 | 0.07 | 0.15 | 0.18 | 0.24 | 0.14 | 0.11 | 0.05 |
Given that the person finds at least 7 songs pleasing to the ear, what is the probability that they find 8 songs pleasing to the ear? Please round to the second decimal point.
In: Statistics and Probability
5.90 Genetics of peas. According to genetic theory, the blossom color in the second generation of a certain cross of sweet peas should be red or white in a 3:1 ratio. That is, each plant has probability 3/4 of having red blossoms, and the blossom colors of separate plants are independent. (a) What is the probability that exactly 8 out of 10 of these plants have red blossoms? (b) What is the mean number of red-blossomed plants when 130 plants of this type are grown from seeds? (c) What is the probability of obtaining at least 90 red-blossomed plants when 130 plants are grown from seeds?
In: Statistics and Probability
Consider a student who is rather irregular about class attendance. If she attends class one day, the probability is .8 that she will attend class the next day. And if she misses class, the probability is .4 that she will miss again the following day.
a. Set up the transition matrix for this stochastic process.
b. If the student attends the first day of class, what is the probability she will miss the third day of class?
c. In the long run what proportion of the time will the student attend class.
d, If student misses class one day, what is the average number of classes going by before she misses
class again.
In: Statistics and Probability
At a call center, calls come in at an average rate of four calls per minute. Assume that the time elapsed from one call to the next has the exponential distribution, and that the times between calls are independent.
a. Find the average time between two successive calls.
b. Find the probability that after a call is received, the next call occurs in less than ten seconds.
c. Find the probability that less than five calls occur within a minute.
d. Find the probability that more than 40 calls occur in an eight-minute period.
e. Find a 95% confidence interval for the number of calls in a minute.
In: Statistics and Probability
Starting at 9 a.m., students arrive to class according to a Poisson process with
parameter λ = 2 (units are minutes). Class begins at 9:15 a.m. There are 30
students.
(a) What is the expectation and variance of the number of students in class by
9:15 a.m.?
(b) Find the probability there will be at least 10 students in class by 9:05 a.m.
(c) Find the probability that the last student who arrives is late.
(d) Suppose exactly six students are late. Find the probability that exactly 15
students arrived by 9:10 a.m.
(e) What is the expected time of arrival of the seventh student who gets
to class?
In: Math
Required to develop a complete C Program (runs in Dev-C++ software) that helps to manage the records of projects in an Engineering Students Design Project competition organized by a university. The actual number of projects are unknown, but it is limited to a maximum number of 100.
Each project record contains information like Project ID, Project Title, Name of Team Members and Scores of evaluation. These project records are stored in a text file, sorted by the project id. A sample text file is given as follows,
| 101; Intelligent vacuum cleaner; Andrew, Bryan and Cecilia;
16;24;20;22; 102; Smart home system; Danesh and Elaine; 18;20;16;21; 104; Rubik's cube solver; Fatimah and Ganesh; 16;22;18;20; |
The criteria of the project evaluation are
(a) Originality and innovativeness: 20%
(b) Scientific approach and technical design: 30%
(c) Result and project outcome: 25%
(d) Presentation and demonstration: 25%
The top three highest scores will be awarded.
In addition, a Best Engineering Design award will be selected based
on criteria (b).
The software reads projects’ details from file, and it should be a
menu driven system having the following minimum options:
1. Add a New Project record (must keep the list ofProject Records sorted by the Project
ID), and update the data file,
2. Print the summary of Project Details, i.e., Project
ID, Title, Members’ Nameand Total Score, ranking from highest to lowest
total score of evaluation,
3. Print the details of the winner Projects, i.e., Project
ID, Title and Members’
Name,
4. Accept query of Project ID, andPrint the Score of evaluation by
criteria.
In: Computer Science
When you make a large purchase (say, a house or a car) you typically borrow money from lenders (e.g. banks, mortgage brokers, credit unions, etc.) who frequently quote the interest you are going to pay in two ways. First, they quote an annual 'interest rate' - the number they widely advertise (but which is often inaccurate), and then a higher (sometimes, much higher) "APR"- which they don't advertise but HAVE to disclose in the fine print because of regulation. The latter number (the "APR") includes all upfront costs generated by the "loan origination" process and reflects your true annualized costs (hence its name "Annual Percentage Rate").
In this discussion, please go online and find two lenders with the largest difference between their APRs (BankRate.com will be useful here) in your area. Make the following assumptions:
1. The value of the house, the down payment, and how much you will borrow.
2. Assume you are taking 30-year fixed mortgage - they are the simplest to deal with.
Calculate the monthly mortgage payments using APRs for both the highest and lowest interest rate lender (or use BankRate's numbers). Calculate the difference in these monthly payments.
Most important: assume that you can invest the DIFFERENCE in monthly payments in the stock market at 0.5% monthly rate of return. How much money would you accumulate by the end of the mortgage (in 360 months) had you invested with the lowest APR lender instead of the highest? What is this value closest to in consumer products? (e.g. iPhone, one-week Hawaii vacation, etc. - be creative).
In: Finance
When you make a large purchase (say, a house or a car) you typically borrow money from lenders (e.g. banks, mortgage brokers, credit unions, etc.) who frequently quote the interest you are going to pay in two ways. First, they quote an annual 'interest rate' - the number they widely advertise (but which is often inaccurate), and then a higher (sometimes, much higher) "APR"- which they don't advertise but HAVE to disclose in the fine print because of regulation. The latter number (the "APR") includes all upfront costs generated by the "loan origination" process and reflects your true annualized costs (hence its name "Annual Percentage Rate").
In this discussion, please go online and find two lenders with the largest difference between their APRs (BankRate.com will be useful here) in your area. Make the following assumptions:
1. The value of the house, the down payment, and how much you will borrow.
2. Assume you are taking 30-year fixed mortgage - they are the simplest to deal with.
Calculate the monthly mortgage payments using APRs for both the highest and lowest interest rate lender (or use BankRate's numbers). Calculate the difference in these monthly payments.
Most important: assume that you can invest the DIFFERENCE in monthly payments in the stock market at 0.5% monthly rate of return. How much money would you accumulate by the end of the mortgage (in 360 months) had you invested with the lowest APR lender instead of the highest? What is this value closest to in consumer products? (e.g. iPhone, one-week Hawaii vacation, etc. - be creative).
In: Finance
Libbey Hocking is the owner of the Hummingbird, an all‐organic restaurant featuring fresh salads and a variety of vegetarian entrée dishes. As part of a dining room redesign, she is replacing all of the glassware in her 100‐seat restaurant. Libbey would like to purchase 40 dozen glasses. Her glassware vendor has offered her similarly styled glassware at three different quality levels. The highest‐quality glassware would cost Libbey $50.00 per dozen. The average life expectancy of these glasses is 1,000 uses before they either break or chip. A lower‐priced, mid‐quality glass sells for $35.00 per dozen and has an expected life of 750 uses. The least expensive glasses sell for $26.00 per dozen and have an expected life of 500 uses. Help Libbey get more information to assess her best purchase choice by completing the following product cost comparison worksheet. (Spreadsheet hint: Format the “Per Use Cost” column to five decimal places). Hummingbird's Glassware Purchase Worksheet Product Durability Price per Dozen Number of Dozens Total Cost Total Number of Glasses Per Glass Cost Estimated Uses per Glass Per Use Cost Highest Middle Lowest Based on cost per use only, which quality glass should Libbey purchase? What nonpurchase price factors might influence Libbey's choice of glassware? If you were Libbey, which product alternative would you select? Explain your answer.
In: Accounting