) a random variable x represent the flight time of an airplane

  

1. A random variable x represent the flight time of an airplane travelling from Cincinnati to New York. Suppose the flight time can be any value in the interval from 80 minutes to 100 minutes and the flight time is said to follow a uniform distribution between 80 and 100 minutes.

(a) Write down the probability density function for the distribution

  

(b) Draw a graph for this probability density function

  

(c) What is the probability that the flight time is between 80 and 90 minutes?

  

(d) Compute the expected value of the random variable x

2. (a) Aside the method of simple sampling, name other sampling methods. 

(b) Give two characteristics of the normal distribution 

3. (a) (5 points) The annual salaries of CEOs in the U.S are normally distributed with a mean, (in thousands) and standard deviation (in thousands). If a CEO is selected at random, what is the probability that his/her annual salary is less than (in thousands)?

(b) (5 points) A population of accountants has a mean annual salary and standard deviation . If a random sampling of is selected from the entire population, find the probability that the sample mean annual salary is greater than 52,000. 

  

Circle the best answer.

1. (2 points) The sampling distribution of the sample mean states that the mean of the sampling distribution of , and standard deviation, for an infinite  

    

2. (2 points) The method of random sampling where each possible sample of size n has same probability of being selected is called

 A standard normal distribution has skewness of measure 1.