Sally plays a game and wins with probability p. Every week, she plays until she wins two games, and then stops for the week. Sally calls it a "lucky week" if she manages to achieve her goal in 7 or less games.

a) If p = 0.2, what's the probability that Sally will have a "lucky week" next week?

b) What's the probability of exactly 3 "lucky weeks" in the next 5 weeks? What's the expected number of "lucky weeks" Sally will have in the next 10 weeks?

c) Let X be the number of games Sally plays in a week, and let q = 1 – p. Find the expectation E[X].

d) If Sally pays $1 to play each game, and gets $5 for each game she wins, what's her expected earning at the end of each week?

Please show all work. A study was undertaken to see how accurate food labeling for calories on food that is considered reduced calorie.  The group measured the amount of calories for each item of food and then found the percent difference between measured and labeled food, .  The group also looked at food that was nationally advertised, regionally distributed, or locally prepared.  The data is in table #11.3.5 ("Calories datafile," 2013).  Do the data indicate that at least two of the mean percent differences between the three groups are different?  Test at the 10% level.

Table #11.3.5: Percent Differences Between Measured and Labeled Food

4. The weights of professional rugby players are normally distributed with mean weight 92 kilograms and standard deviation 12.8 kilograms.

(a) Find the probability that a randomly selected professional rugby player weighs less than 80 kilograms.

(b) Find the probability that a randomly selected professional rugby player weighs over 110 kilograms.

(c) Find the probability that a professional rugby player weighs between 80 and 100 kilograms.

(d) What weight separates the lightest 9% of professional rugby players from the rest?

(e) What weight separates the heaviest 2.5% of professional rugby players from the rest?

An educator wants to determine whether early exposure to school will affect IQ. He enlists the aid of the parents of 12 pairs of preschool-age identical twins who agree to let their twins participate in his experiment. One member of each twin pair is enrolled in preschool for 2 years, while the other member of each pair remains at home. At the end of the 2 years, the IQs of all the children are measured.  

1. Research Hypothesis:
2. Null Hypothesis:
3. Statistical test to use:
4. Degrees of freedom
5. Using α = .05 significance level.

6. Critical value = ________________ Test statistic = ________________

IQ

                                    Twins at                                  Twins at

Pair                             Preschool                                Home

   1                                   120                                         114

   2                                   121                                         118

   3                                   127                                         103

   4                                   117                                         112

   5                                   115                                         117

   6                                   120                                       106

   7                                   130                                         115

   8                                   119                                         113

   9                                   121                                         109

10                                  120                                         112

11                                  117                                         116

12                                  121                                         104

Please help. Show all steps with answers and formulas used.

Create an excel workbook for the following questions. Answer these questions under your Solver work for each respective problem.

1. Devos Inc. is building a hotel. It will have 4 kinds of rooms: suites where customers can smoke, suites that are non-smoking, budget rooms where the customers can smoke, and budget rooms that are non-smoking. When we build the hotel, we need to plan for how many rooms of each type we should have. The following are requirements for the hotel:

1. We want to figure out how many rooms of each type to build based on maximizing revenue if we fill up the hotel. We expect to charge $190 for a suite that is non-smoking and $140 for a budget room that is non-smoking. Smoking room customers for both suites and budget rooms will have to pay an additional $20 per night.
2. We can spend up to $7,500,000 on construction of our hotel. The cost to build a non-smoking budget room is $12,000. The cost to build a non-smoking suite is $15,000. It is $3,000 additional for a smoking room of either type for smoke detectors and sprinklers.
3. We require that the number of budget rooms be at least 1.5 times the number of suites, but no more than 3 the number of suites.
4. There needs to be at least 80 suites, but no more than 200.
5. Industry trends recommend that smoking rooms should be less than 50% of the non-smoking room and in addition, we require our builder gives us at least 4 smoking rooms.

Answer the following using your Solver answers:

1. How many of each room type should be built, and what would the revenue be for a night when our hotel was fully booked?
2. Without re-running Solver, what happens to our revenue if we get an additional $1,500,000 for building? Explain in words how you got this answer without re-running solver. Over what amount of construction costs can you use this procedure?
3. Over what range of room price can our budget non-smoking rooms vary over for us to get the same answer for the quantity of each type of room?

Find the lower z score that bounds the middle 65%? Round to the fourth.

The population proportion is 0.36. What is the probability that a sample proportion will be within ±0.04 of the population proportion for each of the following sample sizes? (Round your answers to 4 decimal places.)

A)n=100

B)n=200

C)n=500

D)n=1000

What is the advantage of a larger sample size?

In a recent survey concerning company sales and net earnings, 15 companies responded with the following information.

a) Using a statistical computing tool, find the equation of the regression line.
For full marks your answer should be accurate to at least three decimal places.

ŷ = ? + ?x

b) Use the regression line from part a to estimate the net earnings for a company with sales of $54.8 thousand.
For full marks your answer should be accurate to at least one decimal place.

Earnings: ?

You are given the sample mean and the population standard deviation. Use this information to construct the 90% and 95% confidence intervals for the population mean. Interpret the results and compare the widths of the confidence intervals. From a random sample of 35 business days, the mean closing price of a certain stock was $105.84. Assume the population standard deviation is $10.29.

Use the SEM formula and show all work.

How satisfied are hotel managers with the computer systems their hotels use? A survey was sent to 400 managers in hotels of size 200 to 500 rooms in Chicago and Detroit. In all, 101 managers returned the survey. Two questions concerned their degree of satisfaction with the ease of use of their computer systems and with the level computer training they had received. The managers responded using a seven-point scale, with 1 meaning "not satisfied", and 4 meaning "moderately satisfied," and 7 meaning "very satisfied".

a. What do you think is the population for this study? What are the major shortcomings in the obtained data?

b. The mean response for satisfaction with ease of use was 5.396. Find the 95% confidence interval for the managers sampled. (Assume the sample SD = 1.75)

c. Provide an interpretation for your answer in part B.

d. For satisfaction with training, the mean response was 4.398. Assuming the sample SD is 1.75, find the 99% confidence interval for the managers sampled.

e. Provide an interpretation of your answer obtained for part D.

A restaurant tried to increase business on Monday night, by featuring a special $1.00 dessert menu. The number of diners on each of 11 Mondays recorded while the special menu was in effect.

The data were

119 139 121 126 128 108 63 118 109 131 142

a. Find a 95% confidence interval the long-run number of diners.

b. Before the special menu, the restaurant average 105.2 diners per Monday night. Is it t reasonable to interpret the confidence interval from part “a” as indicating that the special menu did not increase the average number of diners?

A random sample of 42 taxpayers claimed an average of ​$9,857 in medical expenses for the year. Assume the population standard deviation for these deductions was ​$2,409. Construct confidence intervals to estimate the average deduction for the population with the levels of significance shown below.

a)1%

b)2%

c)20%

The manager of the main laboratory facility at Urban Health Center is interested in being able to predict the overhead costs each month for the lab. The manager believes that total overhead varies with the number of lab tests performed but that some costs remain the same each month regardless of the number of lab tests performed.

After running a regression analysis on the first seven months of the​ year, the manager of the main laboratory facility at Urban Health Center collects seven additional months of data. The number of tests performed and the total monthly overhead costs for the lab​ follow:

Use Excel to do the​ following:

Requirements 1 and 2. Use Excel to run a regression analysis using data for August through February and determine the​ lab's cost equation​ (use the output from the regression analysis you perform using​ Excel). ​(Enter all dollar amounts to two decimal​ places.)

suppose average pizza delivery times are normally distributed with unknown population mean and population standard deviation of 6. A random sample of 28 pizza delivery restaurants is taken and has a sample mean of delivery time of 36 minutes. Show your work.

A. find critical value of 99% confidence level

b. sketch graph

c. what distribution should you use for this problem

d. calculate error bound

e. lower endpoint

upper endpoint