1. A coin is tossed 100 times, each resulting in a tail (T) or a head (H). If a coin results in a head, Roy have to pay Slim 500$. If the coin results in a tail, Slim have to pay Roy 500$. What is the probability that Slim comes out ahead more than $20,000?

Tell how you currently use statistics at a bank. Be descriptive in 250 words or more. Please typed answers only.

Part 1.

When a probability experiment only has two possible outcomes and you know the probability of one outcome, you can find the probability of the other outcome by computing (the complementary probability, using the addition rule, using the multiplication rule)

To find the probability of two (mutually exclusive, independent) events both occurring, you may simply multiply their individual probabilities.

When two scenarios are (mutually exclusive, independent) , we can simply add their probabilities together to find the probability that one scenario or the other scenario occurs.

Part 2.

When using the choose function, the top number n represents (number of successes, number of trials, probability) and the bottom number k represents (number of trials, probability, number of successes )

Part 3.

Suppose you flip a coin 6 times. For each of the 6 trials there are 2 possible outcomes, heads or tails. Heads and tails each have a probability of 0.5 per trial. Consider "heads" to be a success. What is the probability that you only have 2 successes in 6 trials? Round your answer to four digits after the decimal point.

The report "Progress for Children" (UNICEF, April 2005) included the accompanying data on the percentage of primary-school-age children who were enrolled in school for 19 countries in Northern Africa and for 23 countries in Central Africa.

We will construct a comparative stem-and-leaf display using the first digit of each observation as the stem and the remaining two digits as the leaf. To keep the display simple the leaves will be truncated to one digit. For example, the observation 54.6 would be processed as

54.6 → stem = 5, leaf = 4 (truncated from 4.6),

the observation 96.1 would be processed as

96.1 → stem = ? , leaf = ? (truncated from 6.1)

and the observation 35.5 would be processed as

35.5 → stem = ? , leaf = ?(truncated from 5.5).

The resulting comparative stem-and-leaf display is shown in the figure below.

Comparative stem-and-leaf display for percentage of children enrolled in primary school.

From the comparative stem-and-leaf display we can see that there is quite a bit of variability in the percentage enrolled in school for both Northern and Central African countries and that the shapes of the two data distributions are quite different. The percentage enrolled in school tends to be higher in Northern African countries than in Central African countries, although the smallest value in each of the two data sets is about the same. For Northern African countries the distribution of values has a single peak in the 90s with the number of observations declining as we move toward the stems corresponding to lower percentages enrolled in school. For Central African countries the distribution is more symmetric, with a typical value in the mid 60s.

How many individual stem-and-leaf displays are represented by the comparative stem-and-leaf display?

-one

-two     

-three

-It can't be represented as simple stem-and-leaf display.

Paul wants to estimate the mean number of siblings for each student in his school. He records the number of siblings for each of 100 randomly selected students in the school. What is the parameter? Select the correct answer below: all the students in the school the 100 randomly selected students the specific number of siblings for each randomly selected student the mean number of siblings for all students in the school the mean number of siblings for the randomly selected students

Part 1.

About 24% of flights departing from New York's John F. Kennedy International Airport were delayed in 2009. Assuming that the chance of a flight being delayed has stayed constant at 24%, we are interested in finding the probability of 10 out of the next 100 departing flights being delayed. Noting that if one flight is delayed, the next flight is more likely to be delayed, which of the following statements is correct?

• We can use the geometric distribution with n = 100, k = 10, and p = 0.24 to calculate this probability.
• We cannot calculate this probability using the binomial distribution since whether or not one flight is delayed is not independent of another.
• We can use the binomial distribution with n = 100, k = 10, and p = 0.24 to calculate this probability.
• We can use the binomial distribution with n = 10, k = 100, and p = 0.24 to calculate this probability.

Part 2.

A July 2011 Pew Research survey suggests that 27% of adults say they regularly get news through Facebook, Twitter or other social networking sites. What's the probability that in a random sample of 10 people at most 1 of them get their news through social networking sites?

A July 2011 Pew Research survey suggests that 27% of adults say they regularly get news through Facebook, Twitter or other social networking sites. What's the probability that in a random sample of 10 people at most 1 of them get their news through social networking sites?

• 0.20
• 0.96
• 0.16
• 0.04
• 0.06

Part 3.

3.32 Arachnophobia: A 2005 Gallup Poll found that 7% of teenagers (ages 13 to 17) suffer from arachnophobia and are extremely afraid of spiders. At a summer camp there are 10 teenagers sleeping in each tent. Assume that these 10 teenagers are independent of each other.


(a) Calculate the probability that at least one of them suffers from arachnophobia.
(please round to four decimal places)
(b) Calculate the probability that exactly 2 of them suffer from arachnophobia?
(please round to four decimal places)
(c) Calculate the probability that at most 1 of them suffers from arachnophobia?
(please round to four decimal places)

For this problem, carry at least four digits after the decimal in your calculations. Answers may vary slightly due to rounding.

In a random sample of 67 professional actors, it was found that 36 were extroverts.

(a)

Let p represent the proportion of all actors who are extroverts. Find a point estimate for p. (Round your answer to four decimal places.)

(b)

Find a 95% confidence interval for p. (Round your answers to two decimal places.)
lower limit          
upper limit          

Give a brief interpretation of the meaning of the confidence interval you have found.

We are 5% confident that the true proportion of actors who are extroverts falls above this interval.We are 95% confident that the true proportion of actors who are extroverts falls within this interval.     We are 5% confident that the true proportion of actors who are extroverts falls within this interval.We are 95% confident that the true proportion of actors who are extroverts falls outside this interval.

(c)

Do you think the conditions n·p > 5 and n·q > 5 are satisfied in this problem? Explain why this would be an important consideration.

Yes, the conditions are satisfied. This is important because it allows us to say that p̂ is approximately binomial.No, the conditions are not satisfied. This is important because it allows us to say that p̂ is approximately binomial.     Yes, the conditions are satisfied. This is important because it allows us to say that p̂ is approximately normal.No, the conditions are not satisfied. This is important because it allows us to say that p̂ is approximately normal.

Kuantan ATV, Inc. assembles five different models of all-terrain vehicles (ATVs) from various ready-made components to serve the Las Vegas, Nevada, market. The company uses the same engine for all its ATVs. The purchasing manager, Ms. Jane Kim, needs to choose a supplier for engines for the coming year. Due to the size of the warehouse and other administrative restrictions, she must order the engines in lot sizes of 1,000 each. The unique characteristics of the standardized engine require special tooling to be used during the manufacturing process. Kuantan ATV agrees to reimburse the supplier for the tooling. This is a critical purchase, since late delivery of engines would disrupt production and cause 50 percent lost sales and 50 percent back orders of the ATVs. Jane has obtained quotes from two reliable suppliers but needs to know which supplier is more cost-effective. The terms of sale are 5/10 net 30 for Supplier 1 and 3/10 net 30 for Supplier 2. The data related to the costs of ownership associated with two reliable suppliers has been collected in the Microsoft Excel Online file below. Open the spreadsheet and perform the required analysis to answer the questions below.

Questions

1. What is the total cost of ownership for each of the suppliers? Assume the buyer will take advantage of the largest discount. Do not round intermediate calculations. Round your answers to the nearest cent.

2. Which supplier is more cost-effective?

The accompanying data are the number of wins and the earned run averages (mean number of earned runs allowed per nine innings pitched) for eight baseball pitchers in a recent season. Find the equation of the regression line. Then construct a scatter plot of the data and draw the regression line. Then use the regression equation to predict the value of y for each of the given x-values. If meaningful. If the x-value is not meaningful to predict the value of y, explain why not. (a) x=5 wins (b) x=10 wins (c) x=21 wins (d) x=15 wins

The equation of the regression line is y= ? x+? (Round to two decimal places as needed.)

a. Predict the ERA for 5 wins, if it is meaningful.Select the correct choice below and ,if necessary, fill in the answer box within your choice.

A. ^y= ? (Round to two decimal places as needed.)

B. it is not meaningful to predict this value of y because x=5 is well outside the range of the original data.

C. It is not meaningful to predict this value of y because x=5 is not an x-value in the original data.

(b) Predict the ERA for 10 wins, if it is meaningful.Select the correct choice below and, if necessary, fill in the answer box within your choice.

A. y^= ? (Round to two decimal places as needed.)

B. it is not meaningful to predict this value of y because x=10 is not an x-value in the original data.

C. it is not meaningful to predict this value of y because x=10 is inside the range of the orginal data.

(c) Predict the ERA for 21 wins, if it is meaningful. Select the correct choice below and, if necessary, fill in the answer box within your

choice.

A. y^= ? (Round to two decimal places as needed.)

B. It is not meaningful to predict this value of y because x=21 is not x-value in the original data.

C. it is not meaningful to predict this value of y because x=21 is well outside the range of the original data.

(d) Predict the ERA for 15 wins, if it meaningful. Select the correct choice below and,if necessary,fill in the box within your choice.

A. y^= ? (Round to two decimal places as needed.)

B. It is not meaningful to predict this value of y because x=15 is inside the range of the original data.

C. It is not meaningful to predict this value of y because x=15 is not an x-value in the original data.

Wins, x Earned run average, y

20, 2.82

18, 3.24

17, 2.56

16, 3.65

14, 3.79

12, 4.34

11, 3.78

9, 5.07

Moonbucks roasts 2 types of coffee: Guatemala Gold and Sumatra Silver. Each month, the demand for each coffee type is uncertain. For Guatemala Gold, the mean demand is 20,000 pounds and the standard deviation is 5,000 pounds. For Sumatra Silver, the mean demand is 10,000 pounds and the standard deviation is 5,000 pounds. The demand for Guatemala Gold and Sumatra Silver is negatively correlated with a correlation of −0.4, since some customers tend to buy whichever coffee is
on sale that month. It takes time to roast each type of coffee, and both coffees are roasted on the Clover Roasting Machine. The Clover Machine can process 125 pounds of Guatemala Gold per hour, but only 50 pounds of Sumatra Silver per hour. Although the Clover Machine can only roast one of the two coffees at any given moment, it is simple to switch between roasting Guatemala Gold and Sumatra Silver, so there is no setup time required in addition to the roasting times mentioned above.
a. What is the covariance of the demand for Guatemala Gold and the demand for Sumatra Silver?
b. First express T (total roasting time) in terms of G (demand for Guatemala Gold) and S (demand for Sumatra Silver). T = a constant times G plus another constant times S. You need to determine
these constants.
c. What is the expected value of the total roasting time needed to handle the total demand for
Guatemala Gold and Sumatra Silver in one month?
d. What is the variance of the total roasting time needed to handle the total demand for
Guatemala Gold and Sumatra Silver in one month?
e. Moonbuck's operations manager has reserved 640 hours on the Clover Machine to process next
month’s demand. Assuming that total roasting time is normally distributed, do you think this will suffice? What is the probability that 640 hours will be enough?

Each front tire on a particular type of vehicle is supposed to be filled to a pressure of 26 psi. Suppose the actual air pressure in each tire is a random variable—X for the right tire and Y for the left tire, with joint pdf given below. f(x, y) = K(x2 + y2) 22 ≤ x ≤ 30, 22 ≤ y ≤ 30 0 otherwise

(a) Compute the covariance between X and Y. (Round your answer to four decimal places.) Cov(X, Y) =

(b) Compute the correlation coefficient p for this X and Y. (Round your answer to four decimal places.) ρ =

Mid-West Publishing Company publishes college textbooks. The company operates an 800 telephone number whereby potential adopters can ask questions about forthcoming texts, request examination copies of texts, and place orders. Currently, two extension lines are used, with two representatives handling the telephone inquiries. Calls occurring when both extension lines are being used receive a busy signal; no waiting is allowed. Each representative can accommodate an average of 11 calls per hour. The arrival rate is 22 calls per hour.

1. How many extension lines should be used if the company wants to handle 90% of the calls immediately?
   
   
   
2. What is the probability that a call will receive a busy signal if your recommendation in part (a) is used? If required, round your answer to four decimal places.
   
   
   
3. What number of calls, in decimal form, receive a busy signal for the current telephone system with two extension lines? If required, round your answer to four decimal places.
   

Chapter 13

13.1 Jean tests the effects of four different levels of caffeine (no caffeine, 40mg caffeine, 80mg caffeine, 120mg caffeine) on public speaking ability. One group of participants was tested in all four conditions over the course of four weeks – a different condition each week. What statistical analysis should Jean conduct to determine the effect of caffeine on public speaking?

13.2 How does the formula for the repeated-measures ANOVA differ from the formula for the One-way, independent-measures ANOVA?

13.3 Calculate SS_{between subjects} for the following data set. SHOW WORK

Person   Treatment 1       Treatment 2       Treatment 3

A       8           5           7

B       10           4           5

C       6           4           4

D       8           3           6

E       7           6           5

F       8           4           5

13.4 What three hypothesis tests do you have to conduct if you are using a Two-Factor (Factorial) ANOVA to analyze your data? (list/describe each one)

13.5 You can do some basic calculations based on treatment means, to get an idea of what types of effects might be present in a factorial study (even if you can’t say if they are statistically significant). Based on the table of means below, does it look like there could be any main effects or interactions? Specify which ones. SHOW WORK

Use the following scenario and data to answer questions 13.6 - 13.7

Researchers are interested in how serving temperature and pouring method affect the taste of Champagne (more bubbles = better taste). In this 3x2 factorial design, different glasses of Champagne are poured under different conditions; the summary data for the study appear in the table below. The researchers want to know which method is best.

n = 10

N = 60

∑X² = 1150

*Note, low averages mean few bubbles = Champagne is less tasty

13.6 Work through the steps involved in calculating this Factorial ANOVA for the Champagne study. Fill out the ANOVA table below as you go through the steps. Show work for Full Credit and the chance of Partial Credit.

Source               SS           df       MS       F

Between treatments

   Temperature

   Pour

Temperature X Pour

Within treatments

Total

13.7 What critical F value would you use to evaluate the three hypotheses in the Champagne ANOVA?

Temperature critical F =

Pour critical F =

Temperature X Pour critical F =

Chapter 14

14.1 The figure on the right is a scatterplot showing the relationship between drive ratio and horsepower. Based only on the figure, how would you describe this relationship? (Make sure to address its form, direction, and strength.)

Form –

Direction –

Strength –

14.2 What is the biggest limitation a researcher faces when using a correlational design?

14.3 Give one example of a study that would need to use a correlational design?

End of Lab 10!

1. Suppose 50 drug test results are given from people who use drugs (see table below):

If 2 of the 50 subjects are randomly selected without replacement, find the probability that the first person tested positive and the second person tested negative.

_______________

2. A comprehensive final exam in STAT 200 has a mean score of 73 with a standard deviation of 7.8. Assume the distribution of the exam scores is approximately normal. If 24 students are randomly selected, find the probability that the mean of their exam scores is less than 70.

The probability density function of the random variable X is given by fX(x) = ax + 2/9 if 1/2 ≤ x ≤ 3, and 0 otherwise.

(a) Compute the value of a.

(b) Let the random variable Y be defined as Y = [X], where [·] is the “round down” operator (that is, for example, [2.5] = 2, [−2.5] = −3, [−3] = −3). Find the probability mass function of Y . (Hint: For Y to take value k, what values should X take?)

(c) Compute Var(Y )

I am confused with part B.