In your discussion, please answer the below questions: 1. What role does statistics play in calculating the probability of winning the lottery? 2. Why are the combinations of numbers selected important in calculating the probability of wining the lottery? 3. Given the knowledge of calculating the probability of winning a lottery, why do people still buy lottery tickets?

1. Customers arrive at the drive-up window of a fast-food restaurant at a rate of 2 per minute during the lunch hour
   1. What is the probability that the next customer will arrive within 1 minute?
   2. What is the probability that the next customer will arrive after 0.5 minutes?
   3. What is the probability that the next customer will arrive between 45 seconds and 1.5 minutes?

The lengths of lumber a machine cuts are normally distributed with a mean of

104

inches and a standard deviation of

0.6

inch.​(a) What is the probability that a randomly selected board cut by the machine has a length greater than

104.14

​inches?​(b) A sample of

42

boards is randomly selected. What is the probability that their mean length is greater than

104.14

​inches?

​(a) The probability is

Exercise 11

A normal distributed population of measurements has a population mean of 140 and a standard deviation of 8.

• What is the probability that a measurement taken at random in the population will be less than 160?

• What is the probability that a measurement taken at random in the population will be greater than 150?

• What is the probability that a measurement taken at random in the population will be between 150 and 160?

Briefly answer the followings.
a. Explain the differences between probability distribution and sampling distribution.
b. What is the main difference of probability calculation between discrete and continuous random
variables?
c. Compare the characteristics of a t distribution and the standard normal distribution.
d. What do you understand by the statement “The probability density function of a normal
distribution is symmetric.

1.) What is we draw a sample of 225 people from a population with the mean age of 40 and the standard deviation of 24:

1.) What is the probability of getting a sample mean of 38.2 or lower ?

2.) What is the probability of getting a sample mean of 44.5 or higher ?

3.) What is the probability of getting a sample mean between 38.2 and 44.5 ?

Choose an American adult at random. The probability that you choose a woman is 0.52. The probability that the person you choose has never married is 0.25. The probability you choose a woman who has never married is 0.11. Please use this information to answer the following questions.

1. Create a Two-Way Table to visually represent these Events.

Let Prob be a probability function on the power set P(Ω) of a sample space Ω. Let B be a set such that Prob(B) > 0. For any set A, define G(A|B) = Prob(A ∩ B) Prob(B) . Prove that for fixed B and as as a function of A, G(·|B) is also a probability function, meaning that G(·|B) satisfies the axioms of probability..

suppose that you are in a class of 18 students and It is assumed that 15% of the population is left handed.
a. compute probability that exactly 5 students are left handed( 3 decimal places)
b. probability that at most 4 students are left handed (3 decimal places)
c. probability that at least 6 students are left handed (3 decimal places)