11-10-2018

Problem 1. Most computer languages include a function that can be used to generate random numbers. In Excel, the RAND function can be used to generate random numbers between 0 and 1. If we let x denote a random number generated using RAND, then x is a continuous random variable with the following probability density function.

          f(x) = 1     for 0 ≤ x ≤ 1,

                 = 0   otherwise

• 1. Graph the probability density function.

  2. What is the probability of generating a random number between .25 and .75?

  3. What is the probability of generating a random number with a value less than or equal to .30?

  4. What is the probability of generating a random number with a value greater than .60?

Problem 2. Draw a graph for the standard normal distribution. Label the horizontal axis at values of -3, -2, -1, 0, 1, 2, and 3. Then use the table of probabilities for the standard normal distribution inside the front cover of the text to compute the following probabilities.

• 1. P(z ≤ 1.5)

  2. P(z ≤ 1)

  3. P(1≤ z ≤ 1.5)

  4. P(0 < z < 2.5)