MGT 233 - Homework #2 Spring 2018 This homework assignment is due at the beginning of class on Monday, October 8, 2018. 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 Alanarnette.com- Through June of 2017, nearly 5,000 people have summited Mount Everest, located in Nepal. Roughly 25% of the individuals that have summited the highest peak in the world (above sea level) are Sherpas, local people who are hired and paid to help climbers carry tents and cook food at high camps on the summit. In a sample of 15 individuals who have summited Mount Everest: a. How many people do you expect, of those surveyed, to be Sherpas? b. Compute the variance and standard deviation of Sherpas that have summited the peak. c. What is the probability that ten of these individuals are Sherpas? d. What is the probability that six or fewer of these individuals are Sherpas? e. What is the probability that at least thirteen of these individuals are Sherpas? f. What is the probability that ten, eleven, or twelve of these individuals are Sherpas? g. Suppose the rate of individuals who hire Sherpas decreases. Now, only 17% of the individuals who summit the mountain are Sherpas. What is the probability that of the 17 people sampled, exactly 6 of these individuals are Sherpas? (Calculate using the equation)
Problem #2 National Singles Day is a day for everyone, singles and couples alike, to recognize our single friends, family members, co-workers and fellow citizens. The U.S. Census Bureau reports that 45% of U.S. residents age 18+ are single, that s 110.6 million U.S. taxpayers. In 2018, National Singles Day is Saturday, September 22. Assume that the samples below include citizens of The U.S. a. In a sample of 10 individuals, what is the probability that exactly 4 claim they are single? b. In a sample of 12 individuals, what is the probability that at least 8 claim they are single? c. In a sample of 15 individuals, what is the probability that no more than 10 claim they are single? d. In a sample of 9 individuals, what is the probability that 3, 4, 5, or 6, claim they are single?
Problem #3 worldpopulationreview.com - According to the US Census Bureau's population clock, the estimated 2018 United States population (February 2018) is 327.16 million. By population, the United States of America is the third largest country in the world, falling far behind China (1.4 billion) and India (1.25 billion). Over 350 languages are used by the U.S. population in which the four languages spoken at home by the most people. The most commonly used language is English with used by 79.29% of population. Spanish is the second most common language in the country with 12.85%. There is 0.64% using Chinese language, and 7.22% use other languages (Tagalog, Vietnamese, French, Korean, Arabic, and German) Use EXCEL binom.dist.range functions to solve the following probabilities. Show proper probability notation, show the Excel formula used, and carry your work to 5 decimal places. a) In a sample of 10 Americans, what is the probability exactly 4 speak Spanish at home? b) In a sample of 12 Americans, what is the probability that at least 3 speak English at home? c) In a sample of 15 Americans, what is the probability that 8 or fewer speak Chinese at home? d) In a sample of 19 Americans, what is the probability that 3 to 9 do not speak English, Spanish or Chinese at home? e) Using the binom.inv function, when 18 Americans are sampled, there is a 95% probability that less than or equal to how many were spoken Spanish at home?
Problem #4 Himanchal.org, nepalconnection.org.np - The Himanchal Education Foundation is a non-profit organization that exists to promote and advance Mahabir Pun s vision for extended educational opportunities in rural Nepal. HEF originally was founded to support growth of the Nangi school in Nepal. HEF also supports economically sustainable business opportunities and a computer network in Nangi and surrounding villages. Our goal remains to improve the health and life situations for villagers in rural Nepal. Dr. Mahabir Pun earned bachelor and master degrees from UNK. The University of Nebraska Kearney also awarded him with a doctorate of letters for his great accomplishments to advance life in rural Nepal. To help fund schools and health clinics in the mountains of rural Nepal, Dr. Pun opened a wildly successful restaurant in Kathmandu, the capital of Nepal. During trekking/tourist season, the restaurant averages 66 customers during the evening peak hours between 6:00pm and 9:00pm. Use the tables in the textbook for the probabilities. a) How many customer visits are expected in 15 minutes? b) What is the probability of no customers in 6 minutes? c) What is the probability of 5 or fewer customers in 12 minutes? d) What is the probability of 7 or more customers in 18 minutes? e) What is the probability of 6, 7, 8, or 9 customers in 30 minutes?
Problem #5 The Trekking Agencies Association of Nepal (TAAN), launched new treks which will benefit the schools in and around Nangi village. Mahabir Pun has always had the vision of a trekking route close to home. This dream became a reality when the Borderlands Resort s Director Megh Ale agreed to team with the Himanchal Educational Foundation to create this new route. These treks focus on using eco-lodges, conservation, and environmentally sustainable travel. Trekkers will travel for seven days to six villages, whose elevations range from 2,700 feet at the starting point in Beni along the Kali Gandaki River to over 9,000 on the Mohare Ridge. On a clear day you can see over 30 snow clad mountains including three mountains over eight thousand meters (26,000 feet). For a comparison, Pikes Peak in Colorado is 14,114 feet (8,075 feet above Colorado Springs). Eco-Trekking Lodge in Nangi, Nepal In addition to the grandeur of Nepal, these treks are eco-friendly and the lodges are owned and operated by their local schools: all proceeds after expenses go back to the schools for educational purposes and lodges are run by local villagers. October and November are peak trekking season in Nepal, average 890 trekkers visited protected areas each week. But the low season (December and January), on average, only 21 trekkers visited protected areas each week. a) How many trekkers visit protected areas are expected in 28 days in the low season? b) What is the probability of 6 trekkers or fewer visited in three days in the low season? c) What is the probability of more than 7 trekkers visited in one day in the low season? d) What is the probability of 15 to 19 visits in five days in the low season?
Problem #6 Tourism.gov.np- Roughly 940,218 people traveled to Nepal in 2017. During this year, tourism numbers increased by about 25%, the largest increase in the country s history. The government sees the tourism and hospitality industry to be a significant opportunity to improve the economy of the country. Texting with a mobile phone is now a required amenity even for remote rural areas. Assuming Nepal Wireless processes 6,120 text messages per hour during peak times in the rural town of Nangi, Nepal. In Nangi, during peak times: a) how many text messages are expected to be processed in 5 seconds? b) what is the probability that no text messages are sent in 3 seconds? c) what is the probability that 7 or fewer text messages are sent in 4 seconds? d) what is the probability that 5 or more text messages are sent in 5 seconds? e) What is the probability that 17 to 24 text messages are sent in 10 seconds? f) What is the probability that exactly 8 text messages are sent in 2 seconds?
Problem #7 NepalWireless.net - The following story is told by Dr. Mahabir Pun, the Team Leader of Nepal Wireless Networking Project: The Beginning It started with a wish. In 1996. I wished to get Internet in my village for the first time after Himanchal High School got four used computers as presents from the students of a school in Australia. Internet and e-mail were quite new terms then. Turning Point I kept on asking people for ideas. I also wrote a very short e-mail to the BBC in 2001, asking if they knew anybody who could give me ideas (if there were any) to get a cheaper Internet connection to my remote village in Nepal. They took my interview and wrote the articles "Village in the Clouds Embraces Computers" and "Praise for 'Inspirational' Web Pioneer" about my school and the computers we had built in wooden boxes. That article changed everything: I got many responses with ideas from people all over the world. That was the first time I heard about Wi-fi (802.11b) wireless technology. The Network Now Starting in 2002, it has been already 14 years since Nepal Wireless is working in to bring broadband Internet in the rural areas. Our focus is to bring broadband Internet in the rural areas where no commercial Internet Service Providers would like to go. The ultimate goal is to maximize the benefit of the technology to the rural population. Nepal Wireless has built a network spanning 15 districts of Nepal. Altogether, 175 villages are now connected. The Investigation The Nepal Wireless network continually updates the technology while expanding connection to rural mountain villages. Of concern, is the network capacity at the Harmi Relay tower? On average, during peak times the Harmi Relay receives 55 megabytes of digital information per second with a standard deviation of 15 megabytes per second. The Harmi Relay can handle up to 85 megabytes of digital information per second before the system starts buffering. When more than 97 megabytes are received in 1 second, the tower starts dropping data packets. Assume the data arrivals to the Harmi Relay are random and normally distributed. During peak times:
a) What is the probability that the Harmi Relay will receive no more than 49 megabytes in one second? b) What is the probability that the Harmi Relay will receive between 22 and 67 megabytes in one second? c) In a one second period, what is the probability that the Harmi Relay will need to buffer information? d) In any one second, what is the probability that the Harmi Relay will start dropping packets?
Problem #8 Bhutan is the one of five countries which The Himalayas is spread across. It is the last great Himalayan kingdom, shrouded in mystery and magic, where a traditional Buddhist culture carefully embraces global developments. The Bhutanese pride themselves on a sustainable approach to tourism in line with the philosophy of Gross National Happiness. Foreign visitors famously pay a minimum tariff of US$250 per day, making it seem one of the world's more expensive destinations. Tourism in Bhutan has diversified from mostly cultural tourists, sightseers and trekkers to special interests, such as sports and adventure tourism, to ecotourism and nature-based tourism. The average length of stay for tourists in Bhutan is 9.6 days. The standard deviation is 2.75 a) What is the probability that a tourist will stay in Bhutan for 7.8 days or fewer? b) What is the probability that a tourist will stay in Bhutan for 8.9 days or longer? c) In order to stay longer than 99% of the tourists to Bhutan, how long would a tourist need to stay? d) How long would a tourist s stay have to last in order to be in the shortest 10% of visits?
Problem #9 budgetyourtrip.com - Bhutan's strategy of "low volume, high quality" tourism has made it a highly regarded destination among discerning travelers. In an effort to protect Bhutan s environment and culture, the government has placed a minimum fee of $250 per person per day for visitors to Bhutan. The amount that includes land transport, accommodations, food and guide service. Average daily price for travelling a person in Bhutan is $86 with a standard deviation of $25.77. a) What is the probability that people pay more than $140/day? b) What is the probability that a person pay less than $52/day? c) What is the probability that an individual pay between $70 and $120/day?