TV sets: According to the Nielsen Company, the mean number of TV sets in a U.S. household in a recent year was 2.24. Assume the standard deviation is 1.2. A sample of 85 households is drawn.

1. What is the probability that the sample mean number of TV sets is between 2.5 and 3?

2. Find the 30th percentile of the sample mean.

The number of hours per week that high school seniors spend on computers is normally distributed with a mean of 5 hours and a standard deviation of 2 hours. 70 students are chose at random, let x̅ represent the mean number of hours spent on a computer for this group. Find the probability that x̅ is between 5.1 and 5.7.

Consider inserting n distinct keys into a hash table with m buckets, where collisions are resolved by chaining and simple uniform hashing applies.

1. What is the probability that none of the n keys hashed to a particular bucket?

2. What is the expected number of empty buckets?

3. What is the expected number of collisions?

1. The ________________________ of two events A and B is the event that consists of all the elements contained in A and B.
2. If A and B are mutually exclusive then A∩B = _________ and P(A∩B) = ________.
3. If A and B are independent, P(A∩B) = ____________________ (finish the formula).

4.  The law of large numbers says that if an experiment is repeated again and again, the         relative frequency probability will get closer to the _____________________________

5.  If the P(A\B) = 0.6 and P(A∩B) = 0.3, find P(B).

6.  If you roll a single fair die and count the number of dots on top, what is the probability of getting a number of at most 3 on a single throw?

7.  You roll two fair dice, a blue one and a yellow one. Each part has single probability.

1. Find P(odd number on the blue die and even on the yellow die).

     b)  Find P(even on the blue die and greater than 1 on the yellow die).

8.  An urn contains 12 balls identical in every respect except color.  There are 6 red balls, 4 green balls, and 2 blue balls. Each part has single probability.

     a)  You draw two balls from the urn, but replace the first ball before drawing the second.  Find the probability that the first ball is red and the second is green.

     b)  Repeat part (a), but do not replace the first ball before drawing the second.

9.  A computer package sale comes with four different choices of printers and five choices of monitors.  If a store wants to display each package combination that is for sale, how many packages must be displayed?   

10.  You have 100 parts in a box and 25 of them are bad.  What is the probability that:

            a)         the first part you draw will be bad?

            b)         the first part will be good?

            c)         if you draw two parts, both will be good?

1) We are creating a new card game with a new deck. Unlike the normal deck that has 13 ranks (Ace through King) and 4 Suits (hearts, diamonds, spades, and clubs), our deck will be made up of the following.

Each card will have:
i) One rank from 1 to 10.
ii) One of 9 different suits.

Hence, there are 90 cards in the deck with 10 ranks for each of the 9 different suits, and none of the cards will be face cards! So, a card rank 11 would just have an 11 on it. Hence, there is no discussion of "royal" anything since there won't be any cards that are "royalty" like King or Queen, and no face cards!

The game is played by dealing each player 5 cards from the deck. Our goal is to determine which hands would beat other hands using probability. Obviously the hands that are harder to get (i.e. are more rare) should beat hands that are easier to get.a) How many different ways are there to get any 5 card hand?
The number of ways of getting any 5 card hand is  
DO NOT USE ANY COMMAS

b)How many different ways are there to get exactly 1 pair (i.e. 2 cards with the same rank)?
The number of ways of getting exactly 1 pair is
DO NOT USE ANY COMMAS

What is the probability of being dealt exactly 1 pair?
Round your answer to 7 decimal places.


c) How many different ways are there to get exactly 2 pair (i.e. 2 different sets of 2 cards with the same rank)?
The number of ways of getting exactly 2 pair is
DO NOT USE ANY COMMAS

What is the probability of being dealt exactly 2 pair?
Round your answer to 7 decimal places.


d) How many different ways are there to get exactly 3 of a kind (i.e. 3 cards with the same rank)?
The number of ways of getting exactly 3 of a kind is
DO NOT USE ANY COMMAS

What is the probability of being dealt exactly 3 of a kind?
Round your answer to 7 decimal places.


e) How many different ways are there to get exactly 4 of a kind (i.e. 4 cards with the same rank)?
The number of ways of getting exactly 4 of a kind is
DO NOT USE ANY COMMAS

What is the probability of being dealt exactly 4 of a kind?
Round your answer to 7 decimal places.


f) How many different ways are there to get exactly 5 of a kind (i.e. 5 cards with the same rank)?
The number of ways of getting exactly 5 of a kind is  
DO NOT USE ANY COMMAS

What is the probability of being dealt exactly 5 of a kind?
Round your answer to 7 decimal places.


g) How many different ways are there to get a full house (i.e. 3 of a kind and a pair, but not all 5 cards the same rank)?
The number of ways of getting a full house is  
DO NOT USE ANY COMMAS

What is the probability of being dealt a full house?
Round your answer to 7 decimal places.


h) How many different ways are there to get a straight flush (cards go in consecutive order like 4, 5, 6, 7, 8 and all have the same suit. Also, we are assuming there is no wrapping, so you cannot have the ranks be 8, 9, 10, 1, 2)?
The number of ways of getting a straight flush is  
DO NOT USE ANY COMMAS

What is the probability of being dealt a straight flush?
Round your answer to 7 decimal places.


i) How many different ways are there to get a flush (all cards have the same suit, but they don't form a straight)?
Hint: Find all flush hands and then just subtract the number of straight flushes from your calculation above.
The number of ways of getting a flush that is not a straight flush is
DO NOT USE ANY COMMAS

What is the probability of being dealt a flush that is not a straight flush?
Round your answer to 7 decimal places.


j) How many different ways are there to get a straight that is not a straight flush (again, a straight flush has cards that go in consecutive order like 4, 5, 6, 7, 8 and all have the same suit. Also, we are assuming there is no wrapping, so you cannot have the ranks be 8, 9, 10, 1, 2)?
Hint: Find all possible straights and then just subtract the number of straight flushes from your calculation above.
The number of ways of getting a straight that is not a straight flush is  
DO NOT USE ANY COMMAS

What is the probability of being dealt a straight that is not a straight flush?
Round your answer to 7 decimal places.

Answer each sub-question by stating whether the term indicated would increase, decrease, stay the same, or not enough info to say. (Note: “increase” and “decrease” refer to the absolute value.)

a) In the binomial distribution, as N decreases, what happens to the value of the most likely outcome when P = .50?

B. For any N, as P increases from .10 to .50, what happens to the value of the most likely outcome?

C. For any N, as P increases from .50 to .90, what happens to the value of the most likely outcome?

D. When P = .5, what happens to the probability of the most likely individual outcome, as N increases?

E. When P = .8, what happens to the probability of the most likely individual outcome, as N increases?

F. In the binomial distribution, what happens to the value of the most likely individual outcome as N increases and, at the same time, P increases?

G) When P = .5, what happens to the individual probabilities of the very most extreme outcomes (that is, the very highest and lowest possible outcomes) as N increases?

Please show work. Thank You.

1. A school administrator sends out grade school students to sell boxes of candy to raise funds. Below is a selection of four students and the mean number of boxes they sold over a weekend. The administrator wants to calculate the average number of boxes sold across students, but wants to weight this by the number of nearby houses (because students with more houses nearby will sell more boxes). For these data, what is the weighted mean?

2.

What is the average expected number of songs from this sample? (the mean of the probability distribution)

3.

What is the standard deviation of the number of songs from this sample? (the SD of the probability distribution)

4.

What number is at the 55th percentile? (You may round to a whole number for the answer)

The following table shows the number of marriages in a given State broken down by age groups and gender:

                                                            AGE at the time of the marriage

Use the table to answer questions (1) to (11).

1. Use the information in the table to fill in the blanks in the row and column totals.
   

2. How many people (male and female) got married in the State?

3. If a person that was married was randomly chosen, what is the probability that the person was a female less than 20 years old? Express your answer as a percent rounded to the nearest whole percent.

4. If a person that was married was randomly chosen, what is the probability that the person was a male less than 20 years old? Express your answer as a percent rounded to the nearest whole percent.
5. If a person that was married was randomly chosen, what is the probability that the person was between the ages of 25 and 34? Express your answer as a percent rounded to the nearest whole percent.

6. Of the people over the age of 45 who got married, what percentage was female? What percentage was male? Express your answer as a percent rounded to the nearest whole percent.

7. Given that a person married was less than twenty years old, what is the probability that the person was male?

8. Given that a person married was female, what is the probability that the person was between the ages of 35 and 44?

9. If a person that was married was randomly chosen, what is the probability that the person was over the age of 45 or female?

10. If a person that was married was randomly chosen, what is the probability that the person is male and between the ages of 25 and 34?

11. Describe two events, A and B, which are mutually exclusive for the number of marriages in the State. Calculate the probability of each event, and the probability of A or B occurring.

You are the manager of a manufacturing company that produces both plumbuses and dinglebops. Each plumbus is defective with probability .15 and each dinglebop is defective with probability .1. In a case like this, the variance of the number of defective items of each type is as follows. If the defective probability is p, the variance σ^2 is n*p*(1-p).

A) If you produce 500 of each type of item what is the expected number and standard deviation of the TOTAL number of defective items?
Expected number:______
Standard deviation:______

B) Of the 500 plumbuses produced, you will be fired if at least 90 are defective. Assuming the number of defective plumbuses is normally distributed, what is the probability of you being fired?

C) You are now interested in computing the number of plumbuses your company can produce in a day. You collect data over the next 100 days and find the sample mean to be 47 plumbuses and the sample standard deviation to be 9. Compute a 56% confidence interval for the number of plumbuses produced in a day.
( _____ , _____ )

D) A rival manufacturer reports that over 20 days they produced an average of 45 plumbuses per days with a sample standard deviation of 5. You wish to show that your company does better using the information from part C. Carry out a hypothesis test with α = .01 to try to statistically make your case. What is the standard error we should use, what is your p-value, and what is your conclusion?
SE: ____
p-value: ____

Pick one of these conclusions:

Fail to reject the null hypothesis because the p-value is greater than .01

Reject the null hypothesis because the p-value is greater than .01

Fail to reject the null hypothesis because the p-value is less than .05

Reject the null hypothesis because the p-value is greater than .05

Reject the null hypothesis because the p-value is less than .05

Reject the null hypothesis because the p-value is less than .01

Fail to reject the null hypothesis because the p-value is less than .01

Fail to reject the null hypothesis because the p-value is greater than .05

A pair of dice is cast. What is the probability that the sum of the two number landing uppermost is less than 5, if it is known that the sum of the numbers falling uppermost is less than 7?