We usually write numbers in decimal form (or base 10), meaning numbers are composed using 10 different “digits” {0,1,…,9}.{0,1,…,9}. Sometimes though it is useful to write numbers hexadecimal or base 16. Now there are 16 distinct digits that can be used to form numbers: {0,1,…,9,A,B,C,D,E,F}.{0,1,…,9,A,B,C,D,E,F}. So for example, a 3 digit hexadecimal number might be 2B8.

How many 3-digit hexadecimals are there in which the first digit is E or F?

How many 4-digit hexadecimals start with a letter (A-F) and end with a numeral (0-9)?

How many 4-digit hexadecimals start with a letter (A-F) and end with a numeral (0-9)?

In a recent survey, 43 students reported whether they liked their potatoes Mashed, French-fried, or Twice-baked. 24 liked them mashed, 23 liked French fries, and 12 liked twice baked potatoes. Additionally, 11 students liked both mashed and fried potatoes, 9 liked French fries and twice baked potatoes, 10 liked mashed and baked, and 2 liked all three styles. How many students hate potatoes? Explain why your answer is correct.

How many positive integers less than 975 are multiples of 8, 7, or 9? Use the Principle of Inclusion/Exclusion.

We want to build 5 letter “words” using only the first n=12n=12 letters of the alphabet. For example, if n=5n=5 we can use the first 5 letters, {a,b,c,d,e}{a,b,c,d,e} (Recall, words are just strings of letters, not necessarily actual English words.)

1. How many of these words are there total?
2. How many of these words contain no repeated letters?
3. How many of these words start with the sub-word “ade”?
4. How many of these words either start with “ade” or end with “be” or both?
5. How many of the words containing no repeats also do not contain the sub-word “bed”?

1. If all the letters of the word ABOUT are arranged at random in a line, find the probability that the arrangement will begin with AB...

2.   

The odds of throwing two fours on a single toss of a pair of dice is 1:35
What is the probability of not throwing two fours? (Hint: there are 2 conversions here)

All answers are written as fractions for consistency....

Select one:

a. 35/36

b. 1/36

c. 1/35

d. 35/1

Discuss the real–world applications where probabilities are used. (Ex. Stock market trading; Medical treatment plans; etc.)

The null hypothesis plays an important role in significance testing. Explain the concept underlying the null hypothesis and the role it plays in tests of statistical significance (hint: think of the logic involved in the decision making process).

The weights of ice cream cartons are normally distributed with a mean weight of 13 ounces and a standard deviation of 0.6 ounce. ​(a) What is the probability that a randomly selected carton has a weight greater than 13.19 ​ounces? ​(b) A sample of 25 cartons is randomly selected. What is the probability that their mean weight is greater than 13.19 ​ounces?

Please make detailed answers to the problem. So I can understand fully.

Thank you

Question 6:

A market gardener is planning a planting scheme for the new growing season, and there are 12 different crops to choose from – 8 of which are vegetables and 4 of which are grains.

1. a) Calculate the number of different ways he can select 7 crops to plant, if there are no restrictions.
2. b) Redo (a), with the extra restriction that he must select at most 2 grain crops.
3. c) Say that he has selected the following 7 crops: tomatoes, carrots, peas, radishes, beans, lettuce, cilantro. He wishes to plant these in 7 adjacent rows, with 1 crop in each row. Calculate the number of different ways he can arrange these rows, if there are no other restrictions.
4. d) Redo (c), with the extra restriction that the tomatoes and carrots must be planted in adjacent rows.
5. e) Redo (d), with the further extra restriction that the peas and beans must not be planted in adjacent rows.
6. f) Redo (e), with the further extra restriction that the 7 crops must be planted in a circle, instead of in adjacent rows.

1.A particular bank requires a credit score of 640 to get approved for a loan. After taking a sample of 107 customers, the bank finds the 95% confidence interval for the mean credit score is:

662 < μ < 739

Can we be reasonably sure that a majority of people will have a credit score over 640 and be able to get the loan?

• Yes
• No

Why or why not?

2. If n=27, x¯(x-bar)=31, and s=12, construct a confidence interval at a 80% confidence level. Assume the data came from a normally distributed population.

Give your answers to one decimal place.

1. Say 5% of circuit boards tested by a manufacturer are defective. Let Y be the number of defective boards in a random sample of size n = 25.

   1. What kind of random variable is Y ? In particular, write Y ~Distribution(p, n), where you fill in the correct distribution name and parameters p and n.

   2. Determine P (Y ≥ 5).

   3. DetermineP(1≤Y ≤4).

   4. What is the probability that none of the 25 boards are defective?

1. Rejecting the null hypothesis that the population slope is equal to zero or no relationship and concluding that the relationship between x and y is significant does not enable one to conclude that a cause-and-effect relationship is present between x and y. Explain why.

2. Discuss the statistics that must be evaluated when reviewing the regression analysis output. Provide examples of what the values represent and an explanation of why they are important.

Random samples of size n = 330 are taken from a population with p = 0.09.

a. Calculate the centerline, the upper control limit (UCL), and the lower control limit (LCL) for the p⎯⎯p¯ chart. (Round the value for the centerline to 2 decimal places and the values for the UCL and LCL to 3 decimal places.)

Centerline _________

Upper control limit __________

Lower control limit __________

b. Calculate the centerline, the upper control limit (UCL), and the lower control limit (LCL) for the p⎯⎯p¯ chart if samples of 210 are used. (Round the value for the centerline to 2 decimal places and the values for the UCL and LCL to 3 decimal places.)

Centerline_____________

Upper control limit____________

Lower control limit____________

c. Discuss the effect of the sample size on the control limits. (fill in the blanks)

The control limits have a __________ spread with smaller sample sizes due to the _____________ standard error for the smaller sample size.

Textbook publishers must estimate the sales of new​ (first-edition) books. The records indicate that 25​% of all new books sell more than​ projected, 30​% sell close to the number​ projected, and 45​% sell less than projected. Of those that sell more than​ projected, 55​% are revised for a second​ edition, as are 40​% of those that sell close to the number​ projected, and 25​% of those that sell less than projected.

a. What percentage of books published go to a second​ edition?

The taxi and takeoff time for commercial jets is a random variable x with a mean of 8.3 minutes and a standard deviation of 2.2 minutes. Assume that the distribution of taxi and takeoff times is approximately normal. You may assume that the jets are lined up on a runway so that one taxies and takes off immediately after the other, and that they take off one at a time on a given runway. (a) What is the probability that for 36 jets on a given runway, total taxi and takeoff time will be less than 320 minutes? (Round your answer to four decimal places.) (b) What is the probability that for 36 jets on a given runway, total taxi and takeoff time will be more than 275 minutes? (Round your answer to four decimal places.) (c) What is the probability that for 36 jets on a given runway, total taxi and takeoff time will be between 275 and 320 minutes? (Round your answer to four decimal places.)

A random sample of 12 steel ingots was taken from a production line. The masses. in kilograms, of these ingots are given below.

24.8 30.8 28.1 24.8 27.4 22.1

24.7 27.3 27.5 27.8 23.9 23.2

Assuming that this sample came from an underlying normal population, investigate the claim that its mean exceeds 25.0kg

2. Show that the first derivative of the the moment generating function of the geometric evaluated at 0 gives you the mean.

3. Let X be distributed as a geometric with a probability of success of 0.10.

a. Give a truncated histogram (obviously you cannot put the whole sample space on the x-axis of the histogram) of this random variable.

b. Give F(x)

c. Find the probability it takes 10 or more trials to get the first success.

d. Here is a challenge. What is the probability that it takes an even number of trials to get the first success, i.e., P(X=2,4,6,8,...)

Multi-part questions: Packer Fan Tours is the official tour company for the Green Bay Packers of the NFL. One of the events in the package is to sponsor a reception the night before a game for fans that is attended by 5 of the players from the team. There are 53 players on the Green Bay Packers' roster of which 22 are starters. Assume that the 6 players attending the reception this week are chosen randomly. Determine the probability of the following occurring:

a. None of the players at the reception are starters.

b. All of the players at the reception are starters.

c. Two of the players at the reception are starters.

d. Four of the players at the reception are starters.