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L15.2082 - Statistics for Business and Economics (2024/2025)
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The negative binomial distribution can only model independent trials.
Coliform bacteria are randomly distributed in a certain Arizona river at an average concentration of 1 per 20cc of water.
Let X be defined as "number of Coliform bacteria per 20cc of water".
What is the variance of X?
A recent study indicated that 60% of all businesses have a fax machine. The probability that exactly four businesses will have a fax machine in a random selection of six businesses is:
Based on past experience, it is assumed that the number of flaws per foot in rolls of grade-2 paper follows a Poisson distribution with mean of 1 flaw per 5 feet of paper.
What is the probability that in a 12-foot roll there will be at least 1 flaw?
Let be a random variable that follows the binomial distribution with and . Then the probability of the success is,
The World Bank records the prevalence of HIV in countries around the world. According to their data, “Prevalence of HIV refers to the percentage of people ages 15 to 49 who are infected with HIV.” In South Africa, the prevalence of HIV is 17.3%.
Let X = the number of people you test until you find a person infected with HIV.
What is the probability that you must test 30 people to find one with HIV? Present your result with 4 decimal places.
A noisy transmission channel has a per-digit error probability of p = 0.01.
Calculate the probability of more than one error in 10 received digits.
A Quality Control Inspector (QCI) investigates a lot containing 15 skeins of yarn. The QCI randomly samples (without replacement) 5 skeins of yarn from the lot. Let X equal the number of skeins with acceptable color.
Indicate whether the following statement is true or false: "X is a binomial random variable"
A politician believes that 20% of all macroeconomists in senior positions will strongly support a proposal he wishes to advance. Suppose that this belief is correct and that five senior macroeconomists are approached at random.
What is the probability that at least one of the five will strongly support the proposal?