Americans receive an average of 22 Christmas cards each year. Suppose the number of Christmas cards is normally distributed with a standard deviation of 6. Let X be the number of Christmas cards received by a randomly selected American. Round all answers to 4 decimal places where possible.

a. What is the distribution of X? X ~ N(,)

b. If an American is randomly chosen, find the probability that this American will receive no more than 25 Christmas cards this year.

c. If an American is randomly chosen, find the probability that this American will receive between 24 and 27 Christmas cards this year.

d. 76% of all Americans receive at most how many Christmas cards? (Please enter a whole number)

Americans receive an average of 20 Christmas cards each year. Suppose the number of Christmas cards is normally distributed with a standard deviation of 6. Let X be the number of Christmas cards received by a randomly selected American. Round all answers to 4 decimal places where possible.

a. What is the distribution of X? X ~ N(,)

b. If an American is randomly chosen, find the probability that this American will receive no more than 19 Christmas cards this year.  

c. If an American is randomly chosen, find the probability that this American will receive between 21 and 25 Christmas cards this year.  

d. 73% of all Americans receive at most how many Christmas cards? (Please enter a whole number)

An exhibitor at an arts and crafts fair sells only 2 types of products – jams and marinades. When a customer enters the exhibitor’s booth, the exhibitor believes that there is a probability of .40 that the customer would purchase jam. If the customer purchases jam, there a probability of .30 that the customer would also purchase marinade. If the customer does not purchase jam, there is a probability of .5 that the customer would purchase marinade

1. Complete the following probability tree by filling in the blanks with either the appropriate probabilities (to 2 decimal places) or symbols if appropriate. The blanks at the end of each possible outcome is to be filled in with what that outcome represents (e.g., JM would represent the outcome that the customer purchased jam and marinade) The blanks under the column X are to be filled in with the number of types of products purchased (e.g. if the customer purchased 1 of the 2 types of produced you would fill in the number 1 under the column X) Note: If you don’t want to use superscripts, you can use ‘ instead. For example, J^C can be typed as J’.

   Outcome          Prob.         X

                                                                                            M              JM              _______       2

                                                                                       _____

                                                                     J

                                                                                       _____

                                      ­.40                                                                          M^C

                                                                                                        _______         _______      ___

                  _____                             

                                                                                                           M        _______         _______     ___

                                               J^C                _____

                                                                                         _____

                                                                                                                      M^C

_______         _______      ___                 

2. Complete the following statements by inserting the appropriate probabilities (to 4 decimal places if necessay) in the spaces provided.

1. The probability that a customer would purchase either jam or marinade (or both) is _______

2. The probability that a customer would purchase both jam and marinade is ________

3. The probability that the customer purchased jam knowing that if he/she purchased marinade is

_______

Phoenix Marketing identifies Los Angeles Naples and Washington DC as the three US cities with highest percentage of millionaires. Data consistent with the study show the following number of millionaires for sample of individuals from each of the three cities

We intent to Test equality of population proportion of millionaires for these . Test Statistics (X²_calculation) is

If you were assigned the responsibility for selling your firms products on eBay, how would you achieve the highest price? Give five specific ideas. Within your explanation please identify the type of product(s) you plan to sell. You should be very specific; remember you could include selling a multitude of different products (product family). You should consider including the type of pricing strategy you will implement in order to sell the greatest number of products.

The lowest and highest observations in a population are 14 and 48, respectively. What is the minimum sample size n required to estimate μ with 90% confidence if the desired margin of error is E = 1.5? What happens to n if you decide to estimate μ with 95% confidence? (You may find it useful to reference the z table. Round intermediate calculations to at least 4 decimal places and "z" value to 3 decimal places. Round up your answers to the nearest whole number.)

1. Let x be the number of errors that appear on a randomly selected page of a book. The table lists the probability distribution of x.

1. Find the mean of x                                           b) Standard the deviation

2. According to a consulting firm 20% of adults say that they most often use their vacation time for international travel. Assume that this result is true for the current population of all American adults.

1. Using the Binomial formula, find the probability that in a random sample of 12 American
2. adults the number who most often use their vacation time for international travel is

1. Exactly 6

2. None

3. At least 6

4. At most 3

2. Approximate the probability that fewer than 80 have hypertension.

The USF Student Government has seven elected student representatives. Each student representative is equally likely to serve in any of the positions. What is the probability of randomly selecting a President and a vice president?

Group of answer choices 0.024 0.33 0.033 0.002

2. Consider a deck of cards. What is the probability that we observe a red even number card for the first time on the 2nd or 5th draw?

Group of answer choices

0.125

0.237

0.207

0.08

Thirty percent of adults strongly believe the news from social media. You randomly select five adults. Find the probability that the number of adults who strongly believe the news from social media is less than three.

Group of answer choices

0.132

0.163

0.837

0.969

In part (a), show work by writing out the individual probability formulas for P(X = x) and letting C(n,x) = "n choose x" .

Based on 2000 census data, the median annual household income was \$39,000.

(a) Among five randomly selected U.S. households, find the probability that four or more have incomes *exceeding* \$39,000 per year.

Consider a random sample of 16 U.S households for the next 3 questions.

(b) What is the probability of seeing at least 10 of the 16 households with annual incomes under \$39,000? You may use distribution functions in `R` for this one.

(c) What is the expected number of households with annual incomes under \$39,000?

(d) What is the standard deviation of the number of households with annual incomes under \$39,000?

1.) Using excel. A random number generator picks a number from one to nine in a uniform manner.

1. X ~ _________
2. Graph the probability distribution.
3. f(x) = _________
4. μ = _________
5. σ = _________
6. P(3.5 < x < 7.25) = _________
7. P(x > 5.67)
8. P(x > 5|x > 3) = _________
9. Find the 90^th percentile.

2) using excel A subway train on the Red Line arrives every eight minutes during rush hour. We are interested in the length of time a commuter must wait for a train to arrive. The time follows a uniform distribution.

1. Define the random variable. X = _______
2. X ~ _______
3. f(x) = _______
4. μ = _______
5. σ = _______
6. Find the probability that the commuter waits less than one minute.
7. Find the probability that the commuter waits between three and four minutes.