A computer selects a number XX from 4 to 9 randomly and uniformly. Round all answers to 4 decimal places where possible.

1. What is the distribution of XX? XX ~ U(,)
2. Suppose that the computer randomly picks 36 such numbers. What is the distribution of ¯xx¯ for this selection of numbers. ¯xx¯ ~ N(,)
3. What is the probability that the average of 36 numbers will be less than 6?

A company finds that one out of every 5 workers it hires turns out to be unsatisfactory. Assume that the satisfactory performance of any hired worker is independent of that of any other hired workers. If the company hires 15 people, what is the probability that the following number of people will turn out to be satisfactory? (Round your answer to six decimal places.)

exactly 9

A special committee of five professionals is formed from a group of four lawyers, three doctors and three teachers. At least three lawyers are needed in the special committee. Define X as the number of teachers in the special committee.
a) Construct the probability distribution of the random variable X.
b) Calculate the expected of X and provide an interpretation of it.
c) Calculate the standard deviation of X

You roll a fair die three times. What is the probability of each of the​ following?

​a) You roll all 4​'s. ​

b) You roll all even numbers.​

c) None of your rolls gets a number divisible by 3. ​

d) You roll at least one 2.

​e) The numbers you roll are not all 2​'s.

An adult female of species felis catus has given birth to five individuals. The birth weight of the first four young, in grams, are x = 99, 92, 96, 110. Assuming the birth weights of felis catus are normally distributed, what is the probability that the fifth young has a birth weight of 90g or less? (This must be expressed as a number between 0 and 1).

Suppose the number of potholes per randomly select 300 ft stretch of roadway has a Poisson distribution with an average of 4 potholes per 300 ft section of roadway. If we randomly select a 300 ft section of roadway, what is the probability of at least 2 potholes in the section?

a) 0.96

b) 0.02

c) 0.74

d) 0.91

e) 0.93

Demand for Coca Cola at a local restaurant is 60 bottles per day with a standard deviation of 15 bottles per day.

a. Compute the probability that demand will be at most 1700 bottles during the next 28 days.

b. Compute the number of bottles the restaurant should stock to have at most a 9% chance of running out over the next 28 days.

The number of years a radio function is exponentially distributed with parameter λ = 3/8. If Jonas buys a used radio, what is the probability that it will be working after an additional 8 years, if
(a) the radio is at least 3 years old? You are encouraged to use MATLAB for calculation.
(b) the radio is at least 10 years old? You are encouraged to use MATLAB for calculation.

An ordinary (fair) die is a cube with the numbers through on the sides (represented by painted spots). Imagine that such a die is rolled twice in succession and that the face values of the two rolls are added together. This sum is recorded as the outcome of a single trial of a random experiment. Compute the probability of each of the following events.

Event A : The sum is greater than 5 .

Event B: The sum is an even number.