Identify the parameter p in the following binomial distribution scenario. The probability of buying a movie ticket with a popcorn coupon is 0.676, and the probability of buying a movie ticket without a popcorn coupon is 0.324. If you buy 25movie tickets, we want to know the probability that more than 16 of the tickets have popcorn coupons. (Consider tickets with popcorn coupons as successes in the binomial distribution.)

Do you take the free samples offered in supermarkets? About 58% of all customers will take free samples. Furthermore, of those who take the free samples, about 32% will buy what they have sampled. Suppose you set up a counter in a supermarket offering free samples of a new product. The day you were offering free samples, 309 customers passed by your counter. (Round your answers to four decimal places.)

(a) What is the probability that more than 180 will take your free sample?

(b) What is the probability that fewer than 200 will take your free sample?

(c) What is the probability that a customer will take a free sample and buy the product? Hint: Use the multiplication rule for dependent events. Notice that we are given the conditional probability P(buy|sample) = 0.32, while P(sample) = 0.58.

(d) What is the probability that between 60 and 80 customers will take the free sample and buy the product? Hint: Use the probability of success calculated in part (c).

Dartnose College has 4000 students. 30% are first-year students, 25% are sophomores, 25% are juniors, and 20% are seniors. 40% of the first-year students are women, 60% of the sophomores are women, 40% of the jumiors are women, and 60% of the seniors are women. Every student is in one and only one of these classes.

1. What is the probability that a randomly selected student will NOT be a junior?

2. What is the probability that a randomly selected student will be EITHER a junior or a senior?

3. What is the probability that a randomly selected student will be EITHER a woman or a junior?

4. What is the probability that a randomly selected student will be BOTH a senior and a man?

5. If we randomly select three names off the total student list (we might select the same name twice or even three times), what is the probability of picking a woman's name at least once?

6. If we randomly select two names off of the total student list (we might select the same name twice), what is the probability of picking the name of one sophomore and one junior in any order?

2. A survey was given asking the following question “Have you ever been offended by something on social media? The table shows the response give. Using the table below answer the following questions.

Suppose a person is chosen at random from this sample. Show your work by giving the fraction (using the numbers in the table above).   Either round your answers to 4 decimal places or give the fraction reduced to lowest terms.

1. Find the probability that the person is female.

2. Find the probability that the person was offended by something on social media.
   

3. Find the probability that a person was offended, given that the person is female.

4. Find the probability that the person is male, given that the person was not offended.
   
   

5. For this sample, are the events “being offended” and “being male” independent?   Explain your answer by using probabilities.

6. Find the probability of being offended and female.  

7. Find the probability of being offended or female.
   

8. Are the events “female” and “being offended” mutually exclusive? Why or why not?

Do Generation X and Boomers differ in how they use credit​ cards? A sample of 1000

Generation X and 1000 Boomers revealed the results in the accompanying table.

a. If a respondent selected is a member of Generation​ X, what is the probability that he or she pays the full amount each​ month?

b. If a respondent selected is a​ Boomer, what is the probability that he or she pays the full amount each​ month?

c. Is payment each month independent of​ generation?

select which of the following for question C.

A. Payment is not independent of generation because the probability of paying in full does not depend on the​ respondent's generation.

B.Payment is independent of generation because the probability of paying in full does not depend on the​ respondent's generation.

C. Payment is independent of generation because the probability of paying in full depends on the​ respondent's generation.

D.Payment is not independent of generation because the probability of paying in full depends on the​ respondent's generation.

Given a normal distribution with mu equals 100 and sigma equals 10 comma complete parts​ (a) through​ (d). LOADING... Click here to view page 1 of the cumulative standardized normal distribution table. LOADING... Click here to view page 2 of the cumulative standardized normal distribution table. a. What is the probability that Upper X greater than 70​? The probability that Upper X greater than 70 is .0016 nothing. ​(Round to four decimal places as​ needed.) b. What is the probability that Upper X less than 80​? The probability that Upper X less than 80 is nothing. ​(Round to four decimal places as​ needed.) c. What is the probability that Upper X less than 95 or Upper X greater than 125​? The probability that Upper X less than 95 or Upper X greater than 125 is nothing. ​(Round to four decimal places as​ needed.) d. 99​% of the values are between what two​ X-values (symmetrically distributed around the​ mean)? 99​% of the values are greater than nothing and less than nothing.

The mean wait time at Social Security Offices is 25 minutes with a standard deviation of 11 minutes. Use this information to answer the following questions:

A.            If you randomly select 40 people what is the probability that their average wait time will be more than 27 minutes?

B.            If you randomly select 75 people what is the probability that their average wait time will be between 23 and 26 minutes?

C.            If you randomly select 100 people what is the probability that their average wait time will be at most 24 minutes?

2.            The proportion of people who wait more than an hour at the Social Security Office is 28%. Use this information to answer the following questions:

A.            If you randomly select 45 people what is the probability that at least 34% of them will wait more than an hour?

B.            If you randomly select 60 people what is the probability that between 25% and 30% of them will wait more than an hour?

C.            If you randomly select 150 people what is the probability that less than 23% of them will wait more than an hour?

1.            The mean wait time at Social Security Offices is 25 minutes with a standard deviation of 11 minutes. Use this information to answer the following questions:

A.            If you randomly select 40 people what is the probability that their average wait time will be more than 27 minutes?

B.            If you randomly select 75 people what is the probability that their average wait time will be between 23 and 26 minutes?

C.            If you randomly select 100 people what is the probability that their average wait time will be at most 24 minutes?

2.            The proportion of people who wait more than an hour at the Social Security Office is 28%. Use this information to answer the following questions:

A.            If you randomly select 45 people what is the probability that at least 34% of them will wait more than an hour?

B.            If you randomly select 60 people what is the probability that between 25% and 30% of them will wait more than an

hour?

C.            If you randomly select 150 people what is the probability that less than 23% of them will wait more than an hour?

4. Bayes Theorem - One way of thinking about Bayes theorem is that it converts a-priori probability to a-posteriori probability meaning that the probability of an event gets changed based upon actual observation or upon experimental data. Suppose you know that there are two plants that produce helicopter doors: Plant 1 produces 1000 helicopter doors per day and Plant 2 produces 4000 helicopter doors per day. The overall percentage of defective helicopter doors is 0.01%, and of all defective helicopter doors, it is observed that 50% come from Plant 1 and 50% come from Plant 2. [8 points]

(i) The a-priori probability of defective helicopter doors produced by Plant 1 is:

a. 0.0001

b. 0.5

c. 0.002

d. 0.0001 * 0.5

(ii) Probability of helicopter doors produced by Plant 1:

a. 0.5

b. 0.002

c. 0.4

d. 0.2

(iii) Probability of a helicopter door produced by Plant 1 given that the door is defective is:

a. 0.0001

b. 0.5

c. 0.002

d. 0.2 * 0.0001

The table below lists a random sample of 50 speeding tickets on I-25 in Colorado.

Round to the fourth.
a) If a random ticket was selected, what would be the probability that the driver was female?
b) Given that a particular ticket had a male offender, what is the probability that they were more than 20 mph over the limit?
c) Given that a particular ticket was 10-20 mph over the limit, what is the probability that the driver was female?
d) If a random ticket was selected, what would be the probability that the driver was a male?
e) If a random ticket was selected, what would be the probability that the driver is a female and driving 10-20 mph over the limit?
f) If a random ticket was selected, what would be the probability that the driver is a female or driving 0-10 mph over the limit?