Reference no: EM132847872

A subway train on the Red Line arrives every eight minutesuniform distribution.

Define the random variable. 

during rush hour. We are interested in the length of time a commuter must wait for a train to arrive. The time follows a

1. Find f(x), μ and σ. 
2. Find the probability that the commuter waits less than one minute. (Just a number)
3. Find the probability that the commuter waits between three and four minutes. (Just a number)

Historically, a final exam in a course is passed with a probability of 0.9. The exam is given to a group of 70 students. (10 points/5 points each)

1. What are the mean (μ) and standard deviation (σ) of this binomial distribution?
2. Find the probability that at least 69 of the students pass the exam.

The Weather Underground reported that the mean amount of summer rainfall for the northeastern US is at 11.52 inches. 10 cities in the northeast are randomly selected and the mean rainfall amount is calculated to be 10.52 inches with a standard deviation of 1.3 inches.

(1) With a 95% confidence level, can it be concluded that the mean rainfall was the same as the average in the northeastern US?

(2) What if 99% confidence level? do a two tailed t-test and answer those questions.