Jacob is a basketball player who has a 40% probability of successfully making a free throw

(a) In practice, Jacob keeps shooting free throws until he makes one in. Then, he stops and runs a lap.

i. What is the probability that he attempts at most 2 free throws before he has to run a lap?

ii. What is the expected number of free throw attempts Jacob makes before he has to run a lap?

(b) In a game, Jacob attempts 10 free throws.

i. What is the probability that he makes at least 5 free throws in this game?

ii. What is the expected number of free throws made by Jacob in this game?

A store that sells calculators finds that the probability that a calculator breaks is 0.2. The problems with calculators breaking is independent to each calculator. (a) If the store sells 100 calculators, find the probability that 80 of the calculators work and 20 break. (b) From the 100 calculators sold, find the probability that the first 20 calculators sold break and the others work. (c) Suppose, once a calculator breaks down, the store is not allowed to sell any more calculators. What is the expected number of calculators they can sell? (d) Continued from part (c), suppose the store already sold 10 calculators and they all work. What is the expected number of calculators they can sell in total?

4) A pediatrician wishes to recruit 4 couples, each of whom is expecting their first child, to participate in a new natural childbirth regimen. Let p = 0.2 represent the probability that a randomly selected couple agrees to participate.

a) What is the probability that 15 couples refuse to participate before 4 are found who agree to participate?

b) What is the probability that 12 couples refuse to participate before 4 are found who agree to participate?

c) What is the expected value of the total number of couples that must be asked to have 4 participating couples?

d) What is the variance of the total number of couples that must be asked to have 4 participating couples.

Assume we roll a fair four-sided die marked with 1, 2, 3 and 4.
(a) Find the probability that the outcome 1 is first observed after 5 rolls.
(b) Find the expected number of rolls until outcomes 1 and 2 are both observed.
(c) Find the expected number of rolls until the outcome 3 is observed three times.
(d) Find the probability that the outcome 3 is observed exactly three times in 10 rolls
given that it is first observed after 5 rolls.
(e) Find the probability that the outcome 3 is first observed after 5 rolls given that
it is observed exactly three times in 10 rolls

Each member of a random sample of 19 business economists was asked to predict the rate of inflation for the coming year. Assume that the predictions for the whole population of business economists follow a normal distribution with standard deviation 1.5%.

a. The probability is 0.001 that the sample standard deviation is bigger than what number?

b. The probability is 0.05 that the sample standard deviation is less than what number?

c. Find any pair of numbers such that the probability that the sample standard deviation that lies between these numbers is 0.975

Click the icon to view a table of lower critical values for the chi-square distribution. Click the icon to view a table of upper critical values for the chi-square distribution.

You have an urn with 3 balls, some are red and some are blue. Let Bn, n = 0, 1, 2, . . ., denote the number of blue balls at time n. (Then the number of red balls at time n is 3 − Bn.) When we make a transition from time n to time n + 1, we pick one of the balls uniformly at random (i.e., pick each ball with equal probability), and then do one of the following

(a) with probability 1/4 leave this ball in the urn;

(b) with probability 3/4 replace this ball by a ball of opposite color.

Is {Bn, n ≥ 0} is a Markov Chain? If so, what is state space and transition probabilities?

The culinary herb cilantro is very polarizing: Some people love it and others hate it. A large survey of 12,087 American adults of European ancestry asked whether they like or dislike the taste of cilantro. Here are the numbers of men and women in the study for each answer:

1. What is the conditional probability that such an adult likes cilantro, given that the adult is male?     

2. What is the probability that a selected American adult of European ancestry at random is male and dislikes cilantro?   

3. What is the conditional probability that such an adult is female, given that the adult likes cilantro?   

For all these questions, the answer format is .###

You have joined a military supplier building Trident nuclear submarines. You are to engineer the painting process. The painting process generates 3 defects per 100,000 square feet of submarine painted. The submarine has 75,000 square feet of surface area to be painted.

1-This is area. What distribution will you use to analyze number of defects?

2-What is the expected value (m) for the number of defects on one submarine?

3-What is the probability that you will have no defects on a painted submarine?

4-What is the probability that you will have one or more defects on a painted submarine?

5-What is the probability that you will have more than 3 defects?

Consider the following table:

Find the standard deviation of this variable.

Question 5

(CO 4) Twenty-two percent of US teens have heard of a fax machine. You randomly select 12 US teens. Find the probability that the number of these selected teens that have heard of a fax machine is exactly six (first answer listed below). Find the probability that the number is more than 8 (second answer listed below).

Four patients have made appointments to have their blood pressure checked at a clinic. As each patient is selected, he/she is tested. If he/she has high blood pressure, a success (S) occurs; if he/she does not have high blood pressure, a failure (F) occurs. Let x be the number of persons who have high blood pressure (i.e., Let x represent the number of successes among the four sampled persons).

1.             How many outcomes should you have from this probability experiment?
2.             Construct a tree diagram for the number of persons who have high blood pressure
3. List all outcomes from this probability experiment.
4.             What are the possible values for x?
5.             Construct the probability distribution of x.
6. Determine whether the table represents a discrete probability distribution. Explain
7. Find Px=1=
8.             Find Px≤3=
9.               Find Px>2=
10.              Find Px≥2=
11.    Find Px=4=
12. Compte the mean, μ=
13. Compute the variance, σ2=
14. Compute the standard deviation, σ=