R Studio: Underground Gasoline Tanks- Assessment Answer
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Task: 1. A committee of three is to be chosen from a group of four men and five women. Find the probability that the committee contains:- all women [1 marks]
- at least one woman [2 marks]
- exactly two men [1 marks]
- exactly one men, given that at least one man is chosen.
- What is the mean number of the leaking tanks in such sample of 15? [1 mark]
- What is the probability that 10 or more of the 15 tanks leak? [ 1 mark]
- What is the probability that at least 5 of the 15 tanks leak? [1 mark]
- What is the probability that at most 5 of the 15 tanks leak? [1 mark]
- Now you examine a random sample of 1000 tanks nationally, what is the probability at least 275 of these tanks are leaking?
- Read the dataset in R and obtain the frequency distribution. [3 marks]
- Compute the mean number of vehicles that pass the bridge per minute. [2 marks]
- Using part (b) as the lambda value, use the parameter of a Poisson distribution to compute the probabilities for each of the observed values in the frequency distribution. [2 marks]
- Compute the expected frequencies for each of the values in the frequency distribution. [1 mark]
- Compare the expected frequencies to those actually observed values from the “no_vechile.txt”, dataset and comment on your findings (i.e the actual and expected values agree)
- What is the probability that a car picked at random is travelling at more than 100 km/hr?
- What is the probability that a car picked at random is travelling at less than 82 km/hr?
- What is the probability that a car picked at random is travelling between 78 km/hr and 95 km/hr?
- Using the “bank.csv” dataset, check the validity of the statement. Use 5% level of significance. [5 marks]
- Check all assumptions
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