R Studio: Underground Gasoline Assessment Answer

1HAEG

R Programming Assignment Help:

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.

2. Leaking from underground gasoline tanks at service stations can damage the environment. It is estimated that 22% pf these tanks leak. Suppose you examine 15 tanks chosen at random, independent of each other.

• 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?

3. The number of vehicles pass a bridge in one minute interval were recorded over 1000 minutes given in the dataset “no_vechicles.csv”

• 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)

4. A radar unit is used to measure speeds of cars on a motorway. The speeds are normally distributed with a mean of 80 km/hr and a standard deviation of 10 km/hr.

• 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?

5. It is often felt that female account holders have different account balances on average than male account holders.

• Using the “bank.csv” dataset, check the validity of the statement. Use 5% level of significance. [5 marks]
• Check all assumptions

6. Using the “bank.csv” dataset, obtain 95% confidence interval for the average age of the account holders and the average total transaction and interpret them.