MGT 233 Homework #2, Fall 2013

Transcription

1 MGT 233 Homework #2, Fall 2013 This homework assignment is due at the beginning of class on October 15, Instructions: Use proper probability notation for all parts of each problem. Show all work in order to receive full credit. For all normal distribution include a graph indicating the mean and shade the area under investigation. For your own sake be neat. Problem #1 Apple.com Apple has sold a record-breaking nine million new iphone 5s and iphone 5c models, just three days after the launch of the new iphones on September 20. Demand for iphone 5s has exceeded the initial supply, and many online orders are scheduled to be shipped in the coming weeks. According to a survey of more than 4,000 current iphone owners conducted by Ask.com, 45% plan on picking up an iphone 5S or iphone 5C as soon as they hit store shelves. In a sample of 20 current IPhone owners: a) How many people would you expect to upgrade their IPhone? b) Compute the variance and standard deviation of the number of people who are planning to upgrade their IPhones. c) What is the probability that 10 current IPhone user who are planning to buy a new version? d) What is the probability six or fewer IPhone users who are planning to buy a new version? e) What is the probability at least 16 IPhone users who are planning to buy a new version? f) What are the probability 10, 11, or 12 IPhone users who are planning to buy a new version? g) Suppose a corrected news article listed that 46% of current IPhone users will buy the new IPhone. What is the probability that of the 20 people sampled, exactly 5 are planning to buy a new version of IPhone? (calculate using the equation)

2 Problem #2 Money.CNN.com - according the announcement from the Department of Labor, in July2013, the U.S. economy added 162,000 jobs, marking the slowest month for hiring since March. Although the job market has improved over the past few years, it still has a way to go before it fully recovers from the Great Recession. Only about 63% of Americans over age 16 participate in the Job market meaning they have a job or are looking for one. The rate has been hovering recently around its lowest level since If the unemployment rate of 2012 is 5% in Buffalo County, answer the following. a) In a sample of 10 individuals, what is the probability no one is unemployed? b) In a sample of 12 individuals what is the probability that no more than two are unemployed? c) In a sample of 15 individuals, what is the probability that more than two are unemployed? d) In a sample of 9 individuals, what is the probability that 1, 2, or 3 are unemployed?

3 Problem #3 Living.MSN.com Sleep-texting R U 4 real? For a country full of people in need of more sleep, we sure get a lot done while we re snoozing. We walk and talk in our sleep, make sandwiches, go out driving, and even commit crimes. Now sleepdisorder specialists say that texting while sleeping is a burgeoning trend. Between 25 and 35 percent of the 300 students surveyed by Dowdell said they have sent text messages while sleeping, and half admitted allowing technology to interfere with their sleep in some way. US News quotes research from the Pew Internet & American Life Project suggesting that 30% of teens send more than 100 text messages per day and 4 in 5 sleeps with their phone on or near the bed. In a sample of 12 teenagers: a) What is the probability that at least 6 teens send more than 100 text message in a day? b) What is the probability that none of the teens send more than 100 text message in a day? c) What is the probability that fewer than 7 teens sleep with their phone on or near bed? d) What is the probability that 7, 8, 9, or 10 teens sleep with their phone on or near bed? e) What is the probability that all twelve of the teens sleep with their phone on or near bed?

4 Problem #4 Buckle.com headquartered in Kearney, Buckle is a retailer of medium to better-priced casual apparel, footwear, and accessories for fashion-conscious young men and women. Buckle has grown significantly over the past ten years, with the number stores growing to 440. Last year, Buckle sold 5 million pairs of jean during its operating hours (between 10Am to 8Pm) for 360 days. a) How many pairs of jeans does Buckle expect to sell in one hour in a single store? b) How many pairs of jeans does Buckle expect to sell in 30 minutes in a single store? c) What is the probability of exactly 4 pairs of Buckles jeans sell in one hour in a single store? (calculate by hand using the appropriate equation)

5 Problem #5 Themaize.com - Corn is America s No. 1 field crop. In recent years corn production has hit new heights, with over 10 billion bushels harvested. If one year of corn could be stacked end to end, it would be long enough to reach from Earth to Mars! Corn has various usages. More than 40% of corn is used for animal feed and only 10% is used for human consumption. Wal-Mart in Kearney sells 60 packages of corn during the 10-hour daytime peak food shopping period. What is the probability that during the peak food shopping period Wal-Mart will sell: a) No corn in 30 minutes? b) 5 or fewer packages of corns in 2 hours? c) 7 or more packages of corns in 45 minutes? d) 6, 7, 8, or 9 packages in 2.5 hours?

6 Problem #6 CNSNews.com - What would you miss or give up in order to watch the Super Bowl? Fifteen percent of U.S. adults who have a favorite NFL team would miss the birth of their own baby to attend the Super Bowl. Another 19 percent would miss the funeral of a loved one, 20 percent would miss the wedding of a close friend or family member, 21 percent would miss an important work responsibility and 23 percent would give up a vacation in order to watch the Super Bowl. On February 2nd, 2014 the Super Bowl will be at the New Meadowlands Stadium Rutherford, NJ, where gates are inevitability corporate sponsored. One hour before the game, 120 football fans per minute arrive on average at MetLife Gate: a) How many football fans are expected to arrive at MetLife Gate in one second during Super Bowl? b) What is the probability that no one arrive at MetLife Gate in one second? c) What is the probability that t 8 or fewer fans arrive at MetLife Gate in ten seconds? d) What is the probability that 16 or more fans arrive at MetLife Gate in ten seconds? e) What is the probability that 16 to 20 fans arrive at MetLife Gate in ten seconds? f) What is the probability that exactly 18 fans arrive at MetLife Gate in ten seconds?

7 Problem #7 Kaptest.com - GMAT scores are used by business schools to provide a common yardstick to compare candidates for admission. Although the median score is approximately 540, the latest U.S. News and World Report guide reports that the average GMAT scores of the top programs such as Stanford, Sloan, Kellogg and Wharton around 709. GMAT scores are normally distributed. At UNK the MBA (Masters in Business Administration) students have an average GMAT score of 592: a) Suppose you learn that 5% of student that are accepted for an MBA at UNK score of at or below 550 on the GMAT, what is the standard deviation of the score? (round this calculation to two decimal points) b) What is the probability of randomly selecting a student who has a score of at least 600 on the GMAT? c) What is the probability of randomly selecting a student who has a score falling between 575 and 610 on the GMAT? d) The top 3% of the UNK MBA students have at least what GMAT score?

8 Problems # 8 The Home Depot is the world's largest home improvement retailer. It sells an assortment of building materials, home improvement, and lawn and garden products. The company operates in the US, Canada and Mexico. It has 2,252 stores, of which 1,974 stores are located in the US as of January 29, On average a Home Depot customer spends $150 each visit with a standard deviation of $50. Home Depot customer spending patterns are normally distributed. a) What is the probability a Home Depot customer spends $71or less? b) What is the probability that Home Depot customer will spend at least $60? c) What is the probability a Home Depot customer spends between $110 and $180? d) How much would Home Depot customer need to spend to be in the top 99% of all Home Depot customers? e) How much would Home Depot customer need to spend to be in the bottom 10% of all Home Depot customers?

9 Problem #9 Kearney Regional Airport (EAR) is a leading general aviation facility for central Nebraska pilots and businesses. The City oversees all aspects of the airport. It is home to approximately 35 aircraft and handles an estimated 30,000 operations per year, including corporate activity, training and pleasure flying. On average, the time going through airport security at the Kearney Regional Airport is 13 minutes with a standard deviation of 3 minutes. Assume the time going through airport security is normally distributed at Kearney Regional airport. a) What is the probability that the time going through airport security at the Kearney Regional Airport is more than 11 minutes? b) What is the probability that the time going through airport security at the Kearney Regional Airport equal to 10 minutes or less?