A) A coin is tossed and a die is rolled. Draw the tree diagram to list out every possible outcome for this sequence of events. How many total outcomes are possible?

B) Elementary students are given an ID card that has a picture of their face followed by a 4 digit code. Assuming repetitions are allowed, how many ID cards are possible?

C) Six balls are numbered: 1, 2, 3, 5, 8, and 13. A ball is selected, its number recorded, and replaced. Find the expected value for the numbers that will occur. (when needed, round to 4 decimal places)

D) If three coins are tossed, construct the probability distribution for the number of heads that will occur. Then, find the mean (expected value) for the number of heads that occur.

5.34 Number of friends on Facebook. To commemorate Facebook’s 10-year milestone, Pew Research reported several facts about Facebook obtained from its Internet Project survey. One was that the average adult user of Facebook has 338 friends. This population distribution takes only integer values, so it is certainly not Normal. It is also highly skewed to the right, with a reported median of 200 friends. 8 Suppose that σ = 380 and you take an SRS of 80 adult Facebook users. For your sample, what are the mean and standard deviation of x ¯, the mean number of friends per adult user? Use the central limit theorem to find the probability that the average number of friends for 80 Facebook users is greater than 350.

Suppose that a recent poll found that 60​% of adults believe that the overall state of moral values is poor. Complete parts​ (a) through​ (c).

(a) For 400randomly selected​ adults, compute the mean and standard deviation of the random variable​ X, the number of adults who believe that the overall state of moral values is poor.

The mean of X is ___​ (Round to the nearest whole number as​ needed.)

The standard deviation of X is _____ ​(Round to the nearest tenth as​ needed.)

(b) Interpret the mean. Choose the correct answer below.

A.

For every 400 ​adults, the mean is the minimum number of them that would be expected to believe that the overall state of moral values is poor.

B.

For every 240 ​adults, the mean is the maximum number of them that would be expected to believe that the overall state of moral values is poor.

C.

For every 400 ​adults, the mean is the number of them that would be expected to believe that the overall state of moral values is poor.

D.

For every 400 ​adults, the mean is the range that would be expected to believe that the overall state of moral values is poor.

(c) Would it be unusual if 253 of the 400 adults surveyed believe that the overall state of moral values is​ poor?
Yes
No.

About 14​% of the population of a large country is hopelessly romantichopelessly romantic.

If two people are randomly​ selected, what is the probability both are

A) hopelessly romantichopelessly romantic​?

B) What is the probability at least one is hopelessly romantichopelessly romantic​?

Determine whether the random variable is discrete or continuous. In each​ case, state the possible values of the random variable.

​(a) The number of

free dash throw attempts before the first shot is madefree-throw attempts before the first shot is made.

​(b) The

time it takes to fly from City Upper A to City Upper Btime it takes to fly from City A to City B.

please answear all parts

A leading magazine (like Barron's) reported at one time that the average number of weeks an individual is unemployed is 17.2 weeks. Assume that for the population of all unemployed individuals the population mean length of unemployment is 17.2 weeks and that the population standard deviation is 8.1 weeks. Suppose you would like to select a random sample of 190 unemployed individuals for a follow-up study.

Find the probability that a single randomly selected value is between 15.6 and 18.8. P(15.6 < X < 18.8) =

Find the probability that a sample of size n = 190 is randomly selected with a mean between 15.6 and 18.8. P(15.6 < M < 18.8) = Enter your answers as numbers accurate to 4 decimal places.

Use the following results from a test for marijuana​ use, which is provided by a certain drug testing company. Among 141 subjects with positive test​ results, there are 25 false positive results. Among 153 negative​ results, there are 3 false negative results

a. How many subjects were included in the​ study?

b. How many subjects did not use​ marijuana?

c. What is the probability that a randomly selected subject did not use​ marijuana?

Winning the jackpot in a particular lottery requires that you select the correct

four numbers between 1 and 47 ​and, in a separate​ drawing, you must also select the correct single number between 1 and

22. Find the probability of winning the jackpot.

Probability and Statistics
Could you please solve the following questions with specifying the answers

A. If you win $100 for rolling a 12, win $10 for rolling a number less than 6, and lose $4 for rolling anything else, what are your expected winnings per play?

a. $1.94          b. $4.72         c. $2.78         d. -$.68

B. A committee of 7 is be selected from a group of 22 people. How many such committees are possible?

a. 22,254      b. 319,770      c, 170,544     d. 101,458

C. A woman plans on having four children. What is the probability she will have at most 2 boys?

a. 11/16         b. 1/2         c. 9/16        d. 6/16

A certain kind of sheet metal has an average of 6 defects per 13 ft². Assuming a Poisson distribution, we will want to find the probability that a 18 ft² piece of sheet metal has at least 8 defects.

(a) First find the mean number of defects per 18 ft² of this sheet metal. Give your answer as a fraction with no units (for example, if you find the mean to be 34(defects18 ft2)

, then you would type "3/4" in the answer box).
μ = defects18 ft2

(b) Then find the probability that a 18 ft² piece of this sheet metal has at least 8 defects. Round this answer to 4 places after the decimal point, if necessary.
P(at least 8 defects) =

A leading magazine (like Barron's) reported at one time that the average number of weeks an individual is unemployed is 33.9 weeks. Assume that for the population of all unemployed individuals the population mean length of unemployment is 33.9 weeks and that the population standard deviation is 4.9 weeks. Suppose you would like to select a random sample of 218 unemployed individuals for a follow-up study. Find the probability that a single randomly selected value is between 33.7 and 34.1. P(33.7 < X < 34.1) = Find the probability that a sample of size n = 218 n = 218 is randomly selected with a mean between 33.7 and 34.1. P(33.7 < ¯ x x ¯ < 34.1) = Enter your answers as numbers accurate to 4 decimal places.

Using diaries for many weeks, a study on the lifestyles of visually impaired students was conducted. The students kept track of many lifestyle variables including how many hours of sleep obtained on a typical day. Researchers found that visually impaired students averaged 8.818.81 hours of sleep, with a standard deviation of 1.61.6 hours. Assume that the number of hours of sleep for these visually impaired students is normally distributed.

(a)  What is the probability that a visually impaired student gets less than 6.76.7 hours of sleep?

(b)  What is the probability that a visually impaired student gets between 6.66.6 and 7.847.84 hours of sleep?

(c)  Thirty percent of students get less than how many hours of sleep on a typical day?

3. The technology known as 3D printing has come a long way in just a few years, but the machines still tend to be prone to errors that totally ruin what they’re trying to make. A small company has a machine that has a 93% success rate in making a perfect part. Today, they have scheduled to make 25 parts.

a. Does the number of perfect parts follow a binomial model? Check the conditions on page 128. Answer in a complete sentence for each one.

b. Assuming the binomial model does apply, what is the probability that the machine produces 23 or more perfect parts?

c. What is the probability that the machine produces fewer than 20 perfect parts?