Business Statistics

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Mathematics

Business Statistics and Quantitative Analysis

Purdue University Global

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have attached the examples also

Smartphone adoption among American young adults has increased substantially and mobile access to the Internet is pervasive. Fifteen % of young adults who own a smartphone are “smartphone-dependent,” meaning that they do not have home broadband service and have limited options for going online other than their mobile device. (Data extracted from “U.S. Smartphone Use in 2015,” Pew Research Center, April 1, 2015.)

If a sample of American young adults is selected, you can calculate various probabilities. This is a typical binomial probability situation because the young adults are either smart-phone dependent or not. There two possible outcomes which are mutually exclusive and collectively exhausted and satisfy all other properties of the binomial distribution.

Create your own situation that could be modelled with a binomial probability

P(X = x | n, π )

Where:

n = number of observations (the sample)

π = probability of an event of interest

x = number of events of interest in the sample

  1. Define x, n and π in your situation. Select a sample size, n, between 5-20. Select a probability between 0-1 (of course!). Select x that is ≤ n.
  2. Use the Excel function binom.dist to calculate the probability or the workbook (click to download Binomial.xlsx) to create a binomial table. Your binomial table needs to have all possible outcomes included (e.g. x = 0, 1, 2, ... , n).
  3. Copy/paste your binomial table into your post.
  4. Explain in your own words and in the context of your situation, the answer to the question, “What is the probability of P(X = x | n, π )?

See Example post.

First response: Choose a classmate’s post and using their probability table, find the probability such that X ≥ x. How does this probability compare to your classmate’s calculation for X = x? In your own words explain what the difference is and what this probability means in the context of their situation.

See Example post.

Second response: Choose another classmate's post to respond to. Create a question that can be answered using the cumulative probability in their probability table. Answer the question in your own words.

See Example post.

Unformatted Attachment Preview

Unit 2 Discussion Example - Initial Post If a sample of American young adults is selected, you can calculate various probabilities. This is a typical binomial probability situation because the young adults are either smart-phone dependent or not. There two possible outcomes which are mutually exclusive and collectively exhausted and satisfy all other properties of the binomial distribution. Create your own situation that could be modelled with a binomial probability. P(X = x | n, π) Where: n = number of observations (the sample) π = probability of an event of interest x = number of events of interest in the sample 1. Define x, n and π in your situation. Select a sample size, n, between 5-20. Select a probability between 0-1 (of course!). Select x that is ≤ n. 2. Use the Excel function binom.dist to calculate the probability or the workbook (Binomial.xlsx) to create a binomial table. Your binomial table needs to have all possible outcomes included (e.g. x = 0, 1, 2, ... , n). 3. Copy/paste your binomial table into your post. 4. Explain in your own words and in the context of your situation, the answer to the question, “What is the probability of P(X = x | n, π) ? ****************************************************************************************** Smartphone adoption among American young adults has increased substantially and mobile access to the Internet is pervasive. Fifteen percent of young adults who own a smartphone are “smartphone-dependent,” meaning that they do not have home broadband service and have limited options for going online other than their mobile device. (Data extracted from “U.S. Smartphone Use in 2015,” Pew Research Center, April 1, 2015.) 1) In my example of smartphone adoption amount American young adults, Sample size, n = 10 Number of events of interest, x = 3 Probability of event of interest, π = 0.15 = 15% 2) What is the probability that 3 out of my sample of 10 young adults are smartphone dependent? The probability is 0.1298 ≈ 13%. Using the CUMULATIVE tab of the Binomial.xlsx workbook: Binomial Probabilities Table X 0 1 2 3 4 5 6 7 8 9 10 P(X) P( =X) 0.8031 1.0000 0.4557 0.8031 0.1798 0.4557 0.0500 0.1798 0.0099 0.0500 0.0014 0.0099 0.0001 0.0014 0.0000 0.0001 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 Unit 2 Discussion Example - Second Response to a Classmate’s Post Second response: Choose another classmate's post to respond to. Create a question that can be answered using the cumulative probability in their probability table. Answer the question in your own words. ****************************************************************************************** Using the scenario: Smartphone adoption among American young adults has increased substantially and mobile access to the Internet is pervasive. Fifteen percent of young adults who own a smartphone are “smartphone-dependent,” meaning that they do not have home broadband service and have limited options for going online other than their mobile device. (Data extracted from “U.S. Smartphone Use in 2015,” Pew Research Center, April 1, 2015.) Sample size, n = 10 Probability of event of interest, π = 0.15 = 15% What is the probability that 1, 2, 3, 4, or 5 of the 10 young adults’ samples are smartphone dependent? The cumulative probability of 1, 2, 3, 4 or 5, of the 10 young adults sampled is smartphone dependent is 0.9986 = 99.86%. That is pretty high! Binomial Probabilities Table X 0 1 2 3 4 5 6 7 8 9 10 P(X) P( =X) 0.8031 1.0000 0.4557 0.8031 0.1798 0.4557 0.0500 0.1798 0.0099 0.0500 0.0014 0.0099 0.0001 0.0014 0.0000 0.0001 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000
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Explanation & Answer

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Discussion post
Sixty-eight percent of U.S. households, or about 85 million families, own a pet, according
to the 2017-2018 National Pet Owners Survey conducted by the American Pet Products
Association (APPA). This is up from 56 percent of U.S. households in 1988, the first year the
survey was conducted. (Data extracted from Iii.Org, 2018, https://www.iii.org/fact-statistic/factsstatistics-pet-statistics. Accessed 15 June 2018.)
1) In my example of pet ownership in the U.S.,
Sample size, n = 10
Number of events of interest, x = 5
Probability of event of interest, π = 0.68 =...


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