For the data in Data Set #1, generate a Frequency Distribution with an interval size of 10, a lower apparent limit value as a multiple of 10, the largest interval size place on the top of the distribution, and use this distribution to answer questions 11-18.

54 67 88 109 26 33 92 97 32 55 75 81 83 45 21 86 94 100 78 62

What is the midpoint of the lowest interval?

What is the relative frequency of the second lowest interval?

What is the cumulative percentage of the second highest interval?

What is the cumulative frequency of the third lowest interval?

What is the cumulative relative frequency of the third highest interval?

What is the frequency of the highest interval?

For Data Set #1, what would the number of intervals be if you wanted an interval size of 4?

For Data Set #1, what would the interval size be if you wanted 11 intervals?

11. An airline estimates that 90% of people booked on their flights actually show up. If the airline books 82 people on a flight for which the maximum number is 78, what is the probability that the number of people who show up will exceed the capacity of the plane? (binomial probability)

Mimi plans on growing tomatoes in her garden. She has 15 cherry tomato seeds. Based on her experience, the probability of a seed turning into a seedling is 0.30.

(a) Let X be the number of seedlings that Mimi gets. As we know, the distribution of X is a binomial probability distribution. What is the number of trials (n), probability of successes (p) and probability of failures (q), respectively?

(b) Find the probability that she gets at least 5 cherry tomato seedlings. (Round the answer to 3 decimal places) Show all work. Just the answer, without supporting work, will receive no credit.

1. A card is drawn at random from an ordinary deck of 52 playing cards. Describe the sample space if consideration of suits (a) is not, (b) is, taken into account.

2. Answer for b: both a king and a club = king of club.

3. A fair die is tossed twice. Find the probability of getting a 4, 5, or 6 on the first toss and a 1, 2, 3, or 4 on the second toss.

4. Find the probability of not getting a 7 or 11 total on either of two tosses of a pair of fair dice.

5. Two cards are drawn from a well-shuffled ordinary deck of 52 cards. Find the probability that they are both aces if the first card is (a) replaced, (b) not replaced.

6 Find the probability of a 4 turning up at least once in two tosses of a fair die.

7. One bag contains 4 white balls and 2 black balls; another contains 3 white balls and 5 black balls. If one ball is drawn from each bag, find the probability that (a) both are white, (b) both are black,(c) one is white and one is black.

8. Box I contains 3 red and 2 blue marbles while Box II contains 2 red and 8 blue marbles. A fair coin is tossed. If the coin turns up heads, a marble is chosen from Box I; if it turns up tails, a marble is chosen from Box II. Find the probability that a red marble is chosen.

9. A committee of 3 members is to be formed consisting of one representative each from labor, management, and the public. If there are 3 possible representatives from labor,2 from management, and 4 from the public, determine how many different committees can be formed

10. In how many ways can 5 differently colored marbles be arranged in a row?

11. In how many ways can 10 people be seated on a bench if only 4 seats are available?

12.. It is required to seat 5 men and 4 women in a row so that the women occupy the even places. How many such arrangements are possible?

13. How many 4-digit numbers can be formed with the 10 digits 0,1,2,3,. . . ,9 if (a) repetitions are allowed, (b) repetitions are not allowed, (c) the last digit must be zero and repetitions are not allowed?

14. Four different mathematics books, six different physics books, and two different chemistry books are to be arranged on a shelf. How many different arrangements are possible if (a) the books in each particular subject must all stand together, (b) only the mathematics books must stand together?

15. Five red marbles, two white marbles, and three blue marbles are arranged in a row. If all the marbles of the same color are not distinguishable from each other, how many different arrangements are possible?

16. In how many ways can 7 people be seated at a round table if (a) they can sit anywhere,(b) 2 particular people must not sit next to each other?

17. In how many ways can 10 objects be split into two groups containing 4 and 6 objects, respectively?

18. In how many ways can a committee of 5 people be chosen out of 9 people?

19. Out of 5 mathematicians and 7 physicists, a committee consisting of 2 mathematicians and 3 physicists is to be formed. In how many ways can this be done if (a) any mathematician and any physicist can be included, (b) one particular physicist must be on the committee, (c) two particular mathematicians cannot be on the committee?

20. How many different salads can be made from lettuce, escarole, endive, watercress, and chicory?

21. From 7 consonants and 5 vowels,how many words can be formed consisting of 4 different consonants and 3 different vowels? The words need not have meaning.

22. In the game of poker5 cards are drawn from a pack of 52 well-shuffled cards. Find the probability that (a) 4 are aces, (b) 4 are aces and 1 is a king, (c) 3 are tens and 2 are jacks, (d) a nine, ten, jack, queen, king are obtained in any order, (e) 3 are of any one suit and 2 are of another, (f) at least 1 ace is obtained.

23. Determine the probability of three 6s in 5 tosses of a fair die.

24. A shelf has 6 mathematics books and 4 physics books. Find the probability that 3 particular mathematics books will be together.

25. A and B play 12 games of chess of which 6 are won by A,4 are won by B,and 2 end in a draw. They agree to play a tournament consisting of 3 games. Find the probability that (a) A wins all 3 games, (b) 2 games end in a draw, (c) A and B win alternately, (d) B wins at least 1 game.

26. A and B play a game in which they alternately toss a pair of dice. The one who is first to get a total of 7 wins the game. Find the probability that (a) the one who tosses first will win the game, (b) the one who tosses second will win the game.

27. A machine produces a total of 12,000 bolts a day, which are on the average 3% defective. Find the probability that out of 600 bolts chosen at random, 12 will be defective.

28. The probabilities that a husband and wife will be alive 20 years from now are given by 0.8 and 0.9, respectively. Find the probability that in 20 years (a) both, (b) neither, (c) at least one, will be alive.

At a high school football camp the following information kept on each participant. List the highest level of measurement for each category as ratio, interval, ordinal, or nominal. a). Top three college choices - _______________ b). 40 yd Sprint time - ________________ c). Number of push ups - _______________ d). Year of birth - _________________

I am doing a kids fishing game. right now I am doing it with 15 fish and number them 1-5. prize one the lowest value and prize 5 the highest value. What do I need to do for this?

You can work with a partner or by yourself. I want you to invent a game with at least 12 different possible monetary outcomes. These outcomes need to include prizes other than money. You are going to charge people money (you decide how much) to play the game and then you decide how much each outcome is worth (win or lose). Make sure that you are able to find the probability of each outcome (Hint: use dice, deck of cards, etc.) Your goal is to come up with an appealing game that people will want to play, but that you will be the one making money in the end. NO RAFFLES.

Title your game, explain the rules, and list the prizes.

Construct a probability distribution in chart form for your game, your random variable x should represent the player’s monetary outcome (there should be at least 12 different x values). Be sure to subtract what you charged to play from their winnings.

Find the player’s expected value of your game. The expected value needs to be between $-2.00 and $0.00.

Explain how this game is going to make you money, but still be appealing enough for people to try and play.

what is the probability?

A jar contains 4 red marbles, numbered 1 to 4, and 12 blue marbles numbered 1 to 12.

a) A marble is chosen at random. If you’re told the marble is blue, what is the probability that it has the number 2 on it?

b) The first marble is replaced, and another marble is chosen at random. If you’re told the marble has the number 1 on it, what is the probability the marble is blue?

##You have received the phone bill.

##You have 4 phones on your family plan.

##You think that some members of the

##family are using too much data.

##

##You would like to calculate the following

##for each of the family members:

##  lowest number of minutes used

##  highest number of minutes used

##  average number of minutes used

##

##The following list (named phonebill) consists

##of 4 lists, each detailing the name of the family

##member, the number of minutes that family member

##used during the week (7 days) and the phone

##number of that person

phonebill = [

  ["Kiera", [11,21,13,14,15,60,38], "508-111-1110"],

  ["Lorenzo", [20,12,33,26,37,62,70],"508-111-1111"],

  ["Mabel", [31,27,43,7,52,68,5],"508-111-1112"],

  ["Nikolai", [8,7,212,28,114,30,39],"508-111-1113"]

  ]

##you are to calculate the following for each family

##member and append it to the list of information

##for that family member:

##  lowest number of minutes used

##  highest number of minutes used

##  average number of minutes used

##The list phonebill will be as follows after your program executes

[['Kiera', [11, 21, 13, 14, 15, 60, 38], '508-111-1110', 11, 60, 24.571428571428573],

['Lorenzo', [20, 12, 33, 26, 37, 62, 70], '508-111-1111', 12, 70, 37.142857142857146],

['Mabel', [31, 27, 43, 7, 52, 68, 5], '508-111-1112', 5, 68, 33.285714285714285],

['Nikolai', [8, 7, 212, 28, 114, 30, 39], '508-111-1113', 7, 212, 62.57142857142857]

]

Please done in Python format

Problem#: Consider the data shown. Assume that the specifications on this component are 74.05 and 73.95 mm. (a)Estimate process capability for the piston-ring process, for both C_p &C_pk and Estimate the percentage of piston rings produced that will be outside of the specifications?

3. The distribution of results from a cholesterol test has a mean of 180 and a standard deviation of 20. A sample size of 40 is drawn randomly.

a. Find the probability that the sum of the 40 values is greater than 7,550. (Round your answer to four decimal places.

b. Find the sum that is 1.6 standard deviations below the mean of the sums. (Round your answer to two decimal places.)

4. A researcher measures the amount of sugar in several cans of the same soda. The mean is 39.01 with a standard deviation of 0.5. The researcher randomly selects a sample of 100.
a. Find the probability that the sum of the 100 values is greater than 3,909. (Round your answer to four decimal places.)

b. Find the probability that the sum of the 100 values falls between the numbers 3900 and 3910. (Round your answer to four decimal places.

5. An unknown distribution has a mean 12 and a standard deviation of one. A sample size of 25 is taken. Let X = the object of interest.
a. What is the mean of ΣX? (Enter an exact number as an integer, fraction, or decimal.)

b. What is P(Σx < 280)? (Round your answer to five decimal places.)

10. A manufacturer produces 25-pound lifting weights. The lowest actual weight is 24 pounds, and the highest is 26 pounds. Each weight is equally likely so the distribution of weights is uniform. A sample of 100 weights is taken.

a. Find the probability that the mean actual weight for the 100 weights is greater than 24.8. (Round your answer to four decimal places.

b. Find the 95^th percentile for the mean weight for the 100 weights. (Round your answer to two decimal places.)

c. Find the 85^th percentile for the total weight for the 100 weights. (Round your answer to two decimal places.