You are given: Each day, the number of of visitors of an Internet search engine has...
You are given:
Each day, the number of of visitors of an Internet search engine has a distribution with mean 2 million and standard deviation 300000.
The number of searches by each visitor each day has a distribution with mean 5 and variance 4.
The number of visitors of the search engine each day and the number of searches by the visitors are independent.
Using normal approximation for the total number of searches, determine the least number of whole days the search engine should operate so that the prob- ability of having at least 200 million searches will be recorded.
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You are given:
Each day, the number of of visitors of an Internet search engine
has...
2.56 A researcher from a search engine company runs Internet searches and times how long each...
2.56 A researcher from a search engine company runs Internet searches and times how long each one takes. She found that 17 searches took 0.01 to 0.05 seconds; 57 took 0.06 to 0.10 seconds; 134 took 0.11 to 0.15 sec- onds; 146 took 0.16 to 0.20 seconds; 398 took 0.21 to 0.25 seconds; 82 took 0.26 to 0.30 seconds; and 56 took 0.31 to 0.35 seconds. Graph the frequency distribution and comment on its shape. A music teacher held an...
Every day a company makes 100 phone calls. Each call has a 40% chance of being...
Every day a company makes 100 phone calls. Each call has a 40% chance of being answered. Calls are answered or not independently of each other. Every time a call is answered a sale is made in the amount X that is a random variable having a normal distribution with μ= 50 and σ= 5. Let Y be the number of answered calls during a day and let W be the total amount of daily sales. Assume that sales amounts...
Every day a company makes 100 phone calls. Each call has a 40% chance of being...
Every day a company makes 100 phone calls. Each call has a 40% chance of being answered. Calls are answered or not independently of each other. Every time a call is answered a sale is made in the amount X that is a random variable having a normal distribution with μ= 50 and σ= 5. Let Y be the number of answered calls during a day and let W be the total amount of daily sales. Assume that sales amounts...
According to the U.S. National Weather Service, at any given moment of any day, approximately 2000...
According to the U.S. National Weather Service, at any given moment of any day, approximately 2000 thunderstorms are occurring worldwide. Many of these storms include lightning strikes. Sensitive electronic equipment is used to record the number of lightning strikes worldwide every day. 28 days were selected at random, and the number of lightning strikes on each day was recorded. The sample mean was 8.3 million. Assume the distribution of the number of lightning strikes per day is normal and has...
C1: Snow Manufacturing Co. has 6 machines that perform a particular task. Breakdowns occur frequently for this machine. Past records indicate that the number of breakdowns that occur each day is d...
C1: Snow Manufacturing Co. has 6 machines that perform a particular task. Breakdowns occur frequently for this machine. Past records indicate that the number of breakdowns that occur each day is described by the following probability distribution: SK2: 5 marks Number of Probability Breakdowns 0.2 0.3 0.4 More than 3 0.0 Required: 1. What is the expected number of breakdowns in any given day? (2 marks) 2. What is the variance for this distribution? (1 mark) 3. What is the...
A baseball team loses $100,000 for each consecutive day it rains. Say X, the number of...
A baseball team loses $100,000 for each consecutive day it rains. Say X, the number of consecutive days it rains at the beginning of the season, has a Poisson distribution with mean 0.2. What is the expected loss before the opening game?
A survey is carried out to study the number of hours, X, per day spent on using the Internet by the customers of an Internet Service Provider (ISP). Responses from 15 randomly selected customers give the following data:
A survey is carried out to study the number of hours, X, per day spent on using the Internet by the customers of an Internet Service Provider (ISP). Responses from 15 randomly selected customers give the following data:3 2 5 6 1 5 3 4 5 2 4 5 9 5 1(a) Determine the mean and variance of the data set. (b) Is there an outlier in the data set? Justify your answer. (c) Suppose a selected customer is found to spend...
4. Suppose that N is a random variable having a conditional Poisson distribution with ability mass...
4. Suppose that N is a random variable having a conditional Poisson distribution with ability mass function prob- 1 (log 3) PN(i) i 1,2,3,... 2 i (a) Show that the mean of N is 3 log 3 1.6479, 2 and the variance of N is 3(log 3)2 3 log 3 0.7427. 2 4 (b) Calculate the probability P(N -4I 20). (c) Use the Bienaymé-Chebyshev inequality to give a lower bound for the probability that N takes values within 2 standard...
West Edmonton Mall, located in Edmonton, Canada, is the largest shopping mall in North America. The...
West Edmonton Mall, located in Edmonton, Canada, is the largest shopping mall in North America. The mall attracts thousands of shoppers daily. The actual daily visitor number depends on the day and season. Does the cold weather have any effect on the number of visitors, and eventually the retail business of the mall? In order to investigate this, suppose a sample of 6 weekdays was randomly selected from January 2019 to February 2019. The number of shoppers/visitors (in thousands) and...
2. A fire station logs the number of callouts occuring each day for a year and tabulates the results: O < c(c0-8, c1...
2. A fire station logs the number of callouts occuring each day for a year and tabulates the results: O < c(c0-8, c1-12, c2-36, c3-54 , c4-67 , c5-66, с7-37, c8-23, с9-10 , с10-11) c6-41, This means that on 8 days there were zero callouts, on 12 days there was one callout, on 36 days there were two callouts, and so on up to 11 days when there were 10 callouts. We wish to test the hypothesis that the number...
2.56 A researcher from a search engine company runs Internet searches and times how long each one takes. She found that 17 searches took 0.01 to 0.05 seconds; 57 took 0.06 to 0.10 seconds; 134 took 0.11 to 0.15 sec- onds; 146 took 0.16 to 0.20 seconds; 398 took 0.21 to 0.25 seconds; 82 took 0.26 to 0.30 seconds; and 56 took 0.31 to 0.35 seconds. Graph the frequency distribution and comment on its shape. A music teacher held an...
C1: Snow Manufacturing Co. has 6 machines that perform a particular task. Breakdowns occur frequently for this machine. Past records indicate that the number of breakdowns that occur each day is described by the following probability distribution: SK2: 5 marks Number of Probability Breakdowns 0.2 0.3 0.4 More than 3 0.0 Required: 1. What is the expected number of breakdowns in any given day? (2 marks) 2. What is the variance for this distribution? (1 mark) 3. What is the...
4. Suppose that N is a random variable having a conditional Poisson distribution with ability mass function prob- 1 (log 3) PN(i) i 1,2,3,... 2 i (a) Show that the mean of N is 3 log 3 1.6479, 2 and the variance of N is 3(log 3)2 3 log 3 0.7427. 2 4 (b) Calculate the probability P(N -4I 20). (c) Use the Bienaymé-Chebyshev inequality to give a lower bound for the probability that N takes values within 2 standard...
West Edmonton Mall, located in Edmonton, Canada, is the largest shopping mall in North America. The mall attracts thousands of shoppers daily. The actual daily visitor number depends on the day and season. Does the cold weather have any effect on the number of visitors, and eventually the retail business of the mall? In order to investigate this, suppose a sample of 6 weekdays was randomly selected from January 2019 to February 2019. The number of shoppers/visitors (in thousands) and...
2. A fire station logs the number of callouts occuring each day for a year and tabulates the results: O < c(c0-8, c1-12, c2-36, c3-54 , c4-67 , c5-66, с7-37, c8-23, с9-10 , с10-11) c6-41, This means that on 8 days there were zero callouts, on 12 days there was one callout, on 36 days there were two callouts, and so on up to 11 days when there were 10 callouts. We wish to test the hypothesis that the number...
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