A random variable X follows the continuous uniform distribution with a lower bound of −2 and an upper bound of 16. a. What is the height of the density function f(x)? (Round your answer to 4 decimal places.) b. What are the mean and the standard deviation for the distribution? (Round your answers to 2 decimal places.) c. Calculate P(X ≤ 1). (Round intermediate calculations to at least 4 decimal places and final answer to 4 decimal places.)

a. Height=0.0555

b. Mean=7

SD=4.0415

c. P(x≤1)=0.1665

Step-by-step explanation:

a. If we have a continous uniform distribution, we have a density function that is a constant:

In the other hand, the cumulative density function across the entire region should be one:

Then the height C of the density function is 0.0555.

b. The mean of this distribution is:

The standard deviation of this distribution is:

c.

answer: 8

step-by-step explanation: if you add the possibilities 5 different flavor and 3 different sizes 5+3=8