4.1 Hypergeometric Distribution
The following activities and questions relate to material covered in Chapter 4.1 Hypergeometric Distribution in Introductory Business Statistics (OpenStax).
Data sets for the following questions are available in Excel: 4.1 Data Sets [XLSX].
Questions
- A member of the YT Elites Volleyball Club has a volleyball practice four days a week. She practices for all of the four days 87% of the time, three days 6% of the time, two days 4% of the time, one day 2% of the time, and no days 1% of the time. Suppose one week is randomly selected.
- Define the random variable X.
- Construct a probability distribution table for the data.
- We know that for a probability distribution function to be discrete, it must have two characteristics. One is that the sum of the probabilities is one. What is the other characteristic?
- Valerie volunteers at the local territorial farmer’s market no more than 7 hours and no less than 1 hour, per week. She volunteers 7 hours 42% of this summer, 6 hours 29% of this summer, 5 hours 10% of this summer, 4 hours 7% of this summer, 3 hours 6% of this summer, 2 hours 4% of this summer, and 1 hour 2% of this summer.
- Define the random variable X.
- What values does X take on?
- Construct a table to organize the data.
- Find the probability that Valerie volunteers for more than 5 hours, per week.
- Find the probability that Valerie volunteers for at most 3 hours, per week.
- Over the last 13 years, Yukon University, has averaged 5,574 students enrolled, per year. Of these enrollments 11.35% are full-time credit students, 10.15% are part-time credit students, and 78.49% are non-credit students. One student is selected at random. Data source: Yukon University. Fast facts, Credit program enrolment. (2021). https://www.yukonu.ca/about-us/publications-plans-reports/institutional-research/fast-facts
- Define the Random Variable, is it discrete or continuous?
- Use the data to construct a probability distribution table.
- What is the probability that the student will be enrolled in credit courses?
- What are the two characteristics required for a probability distribution function to be discrete?
Solutions
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- Let x be the number of days volleyball member attends the practice per week.
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x P(x) 0 0.01 1 0.02 2 0.04 3 0.06 4 0.87 - Each probability is between zero (0) and one (1), inclusive.
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- Let X = the number of hours Valerie volunteers at the market.
- The values that X takes on are the number of hours Valerie volunteers at the market. X = 1, 2, 3, 4, 5, 6, 7
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X P(X) (%) 1 2 2 4 3 6 4 7 5 10 6 29 7 42 - P(X > 5) = 29% + 42% = 71%.
The probability that Valerie volunteers for more than 5 hours per week is 71%. - P(X < 3) = 2% + 4% + 6% = 12%.
The probability that Valerie volunteers for at most 3 hours per week is 12%.
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- The discrete random variable is the type of program the student is enrolled in. (FT, PT, NC)
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X P(X) Full-time 0.1135 Part-time 0.1015 Non-credit 0.7849 - There is a 11.35% + 10.15% = 21.51% chance the randomly selected student will be enrolled in credit courses.
- Each probability is between 0 and 1, inclusive. The sum of probabilities is 1.