A survey asked parents of children aged ten and under how many birthday parties they attended last year. Let X represent the number of birthday parties. The probability distribution is given below. Find the mean and the standard deviation of the probability distribution using Excel. Round the mean and standard deviation to three decimal places.

x P(x) 1 0.0303 2 0.0639 3 0.0197 4 0.003 5 0.0164 6 0.0454 7 0.0981 8 0.0648 9 0.0657 10 0.0124 11 0.0118 12 0.0539 13 0.0497 14 0.0648 15 0.0373 16 0.0475 17 0.0224 18 0.0191 19 0.0088 20 0.0406 21 0.0445 22 0.1202 23 0.0597

Provide a rationale as to why the three (3) aforementioned concepts or skills are important to someone in the field of business statistics.

1. Common Cause vs Special Cause Variation
2. SIPOC Model
3. Basic Improvement & Problem Solving Frameworks

1. The data below are survival times (in years) for cancer patients receiving experimental therapy (TREAT) or standard of care (SOC) in a time-to-mortality study.

1. By hand, calculate the Kaplan-Meier estimate of the survival function for each therapy:
2. By hand, calculate the pointwise 95% confidence intervals for the Kaplan-Meier survival estimate for each therapy.
3. By hand, calculate the point and 95% confidence interval estimates of the 25^th, 50^th, and 75^th percentiles of the survival distribution for each therapy.

1. QD Corporation makes paints known for their quality and quick drying features. QD has developed a new wall paint code named Mickey that it is testing in a controlled environment. The firm is testing for drying time of the paint. Drying time is affected by factors like humidity, air pollution, ventilation and temperature. The test results show that the drying time of Mickey is normally distributed with a mean of 10 hours and a standard deviation of 1.8 hours.

Compute the following:

1. What is the probability that the drying time is less than 7 hours?
2. What is the probability that the drying time is between 6 hours and 12 hours?
3. What should the label on the paint can say if the firm wants to be 95% sure that the drying time will be the claimed time or less?
4. A customer returns a can saying that the drying time was 15 hours. What is the z score corresponding to that observed value?

4.3. Referring to the previous problem, again suppose that a uniform prior is placed on the proportion π, and that from a random sample of 327 voters, 131 support the sales tax. Also suppose that the newspaper plans on taking a new survey of 20 voters. Let y∗ denote the number in this new sample who support the sales tax.

1. Find the posterior predictive probability that y∗ = 8.

2. Find the95% posterior predictive interval for y∗.Do this by finding the predictive probabilities for each of the possible values of y∗ and ordering them from largest probability to smallest. Then add the most probable values of y∗ into your probability set one at a time until the total probability exceeds 0.95 for the first time.

In the average month there is about 150,000 trucks sold across the board. There is about 350,000 vehicles sold every month. Trucks make up about 43% of the sales every month in the USA. At a 95% confidence level there are between ____% and ____% trucks sold every month.

Dixie Showtime Movie Theaters, Inc., owns and operates a chain of cinemas in several markets in the southern U.S. The owners would like to estimate weekly gross revenue as a function of advertising expenditures. Data for a sample of eight markets for a recent week follow.

(a) Use the data to develop an estimated regression with the amount of television advertising as the independent variable. Let x represent the amount of television advertising. If required, round your answers to three decimal places. For subtractive or negative numbers use a minus sign even if there is a + sign before the blank. (Example: -300)

(b) How much of the variation in the sample values of weekly gross revenue does the model in part (a) explain? If required, round your answer to two decimal places.

(c) Use the data to develop an estimated regression equation with both television advertising and newspaper advertising as the independent variables. Let x1 represent the amount of television advertising. Let x2 represent the amount of newspaper advertising. If required, round your answers to three decimal places. For subtractive or negative numbers use a minus sign even if there is a + sign before the blank. (Example: -300)

(d) How much of the variation in the sample values of weekly gross revenue does the model in part (c) explain? If required, round your answer to two decimal places. %

Two players (player A and player B) are playing a game against each other repeatedly until one is bankrupt. When a player wins a game they take $1 from the other player. All plays of the game are independent and identical. a) Suppose player A starts with $2 and player B starts with $1. If player A wins a game with probability p, what is the probability that player A wins all the money? b) Suppose player A starts with $6 and player B starts with $6. If player A wins a game with probability 0.5, what is the probability the game ends (someone loses all their money) on exactly the 10th play of the game?

For the random variables below, indicate whether you would expect the distribution to be best described as geometric, binomial, Poisson, exponential, uniform, or normal. For each item, give a brief explanation of your answer.

a) The number of heads in 13 tosses of a coin.

b) The number of at-bats (attempts) required for a baseball player to get his first hit.

c) The height of a randomly chosen adult female.

d) The time of day that the next major earthquake occurs in Southern California.

e) The number of automobile accidents in a town in one week.

f) The amount of time before the first score in a lacrosse game.

g) The number of times a die needs to be rolled before a 3 appears.

h) The number of particles emitted by a radioactive substance in five seconds.

The quality control manager of Ridell needs to estimate the mean breaking point of a large shipment of helmets sent to the Philadelphia Eagles. Given the production process, the known standard deviation of the population of breaking points is 15.5 lbs. A random sample of 49 helmets were selected and subjected to increasing pressure until every one of them broke. The breaking point of each helmet was recorded, and average breaking point of the sample was 150 lbs.

What are the critical values from the z distribution associated with a 95% confidence interval?

n a study designed to test the effectiveness of magnets for treating back​ pain, 3535 patients were given a treatment with magnets and also a sham treatment without magnets. Pain was measured using a scale from 0​ (no pain) to 100​ (extreme pain). After given the magnet​ treatments, the 3535 patients had pain scores with a mean of 12.0 and a standard deviation of 2.2. After being given the sham​ treatments, the 3535 patients had pain scores with a mean of 10.2 and a standard deviation of 2.6

Construct the 90​% confidence interval estimate of the mean pain score for patients given the sham treatment.

What is the confidence interval estimate of the population mean μ​?

The distribution of heights of adult men in the U.S. is approximately normal with mean 69 inches and standard deviation 2.5 inches. Use what you know about the EMPIRICAL RULE to answer the following.

a)Approximately what percent of men are taller than 69 inches?

b)Approximately what percent of men are between 64 and 66.5 inches?

Find the sample size necessary to estimate the mean IQ score of statistics students such that it can be said with 95​% confidence that the sample mean is plus or minus3 IQ points of the true mean. Assume that the standard deviation is 15 and determine the required sample size.

2)

In a survey of

2,416 adults, 1,876 reported that​ e-mails are easy to​ misinterpret, but only 1,231 reported that telephone conversations are easy to misinterpret. Complete parts​ (a) through​ (c) below.

a. Construct a​ 95% confidence interval estimate for the population proportion of adults who report that​ e-mails are easy to misinterpret.

EXERCISES ON DISCRETE DISTRIBUTIONS

6. An exam consists of 12 questions that present four possible answers each. A person, without knowledge about the subject of the exam, answers the random exam questions.
a.What is the probability that you get the right answer when answering a question?
b. Find the probability that such person does not answer any questions well
C. Calculate the probability of correcting a question.
d. Obtain the probability that you answer all the questions correctly.
e. Obtain the probability of answering more than half of the questions correctly

1. Identify the possible values of each of the 3 variables in this dataset and describe what information each of the 3 variables tells us about the data