A hotel in Saint Augustine books an average of 50 rooms per night. There is a standard deviation of 10 rooms per night. What is the probability that...

a) more than 50 rooms are booked on a given night?

b) between 50 and 60 rooms are booked on a given night?   

c) 60 rooms or less are booked on a given night?   

d) between 30 and 70 rooms are booked on a given night?

e) less than 40 rooms are booked on a given night?

Because of staffing decisions, managers of the Gibson-Marimont Hotel are interested in the variability in the number of rooms occupied per day during a particular season of the year. A sample of 29 days of operation shows a sample mean of 300 rooms occupied per day and a sample standard deviation of 35 rooms.

1. What is the point estimate of the population variance?
   
   
2. Provide a 90% confidence interval estimate of the population variance (to 1 decimal).
   (  ,  )
   
3. Provide a 90% confidence interval estimate of the population standard deviation (to 1 decimal).
   (  ,  )

a) In order to determine the average price of hotel rooms in Atlanta. Using a 0.1 level of significance, we would like to test whether or not the average room price is significantly different from $110. The population standard deviation is known to be $16. A sample of 64 hotels was selected. The p-value associated with the test statistic (z) is calculated and it is 0.03. We conclude that the average price of hotel rooms in Atlanta is NOT significantly different from $110. (Enter 1 if the conclusion is correct. Enter 0 if the conclusion is wrong.)

b) A sample of 27 account balances of a credit company showed an average balance of $1,169 and a standard deviation of $139. You want to determine if the mean of all account balances is significantly greater than $1,150. Use a 0.05 level of significance. Assume the population of account balances is normally distributed. Compute the test statistic.

c) A sample of 30 account balances of a credit company showed an average balance of $1,170 and a standard deviation of $125. You want to determine if the mean of all account balances is significantly greater than $1,150. Assume the population of account balances is normally distributed. Compute the p-value for this test.

d) A sample of 28 account balances of a credit company was taken to test whether the mean of all account balances is significantly greater than $1,150. Using the sample standard deviation, the test statistic (t) was calculated to be $1.89. We use a 0.05 level of significance. Assume the population of account balances is normally distributed and the population standard deviation is unknown to us. We conclude that the mean of all account balances is significantly greater than $1,150. (Enter 1 if the conclusion is correct. Enter 0 if the conclusion is wrong.)

The manager of alarge hotel on the Riviera in southern France wanted to forecast the monthly vacancy rate (as a percentage) during the peak season.   After considering a long list of potential variables, she identified two variables that she believed were most closely related to the vacancy rate: the average daily temperature and the value of the currency in American dollars. She collected data for 23 months.

                  a.   Perform a regression analysis using a first-order model with interaction.

                  b.   Perform a regression analysis using a second-order model with interaction.

                  c.   Which model fits better? Explain.

Suppose the guests at the hotel have an average weight of 180 with a standard deviation of 50 pounds. An elevator is designed to carry only 10 people with a maximum capacity of 2400 pounds.

5. What is the mean of the sample mean?

6. What is the standard deviation for the sample mean of the 10 people? (Use 2 decimals)

7. If 10 guest ride the elevator at one time, what is the probability that the elevator is overweight? (Hint: If the 10 people weigh more than 2400 pounds, how much does each person have to weigh on average? (Use 4 decimals)

8. If 12 guests ride in the elevator at one time, now what is the probability that the elevator is overweight? (Hint: the standard deviation also changes here) (Use 4 decimals)

According to a research​ institution, the average hotel price in a certain year was

​$107.64

.

Assume the population standard deviation is

​$20.00

and that a random sample of

46

hotels was selected. Complete parts a through d below.

a. Calculate the standard error of the mean.

sigma Subscript x overbar

equals​$nothing

​(Round to two decimal places as​ needed.)

b. What is the probability that the sample mean will be less than

​$109

​?

Upper P left parenthesis x overbar less than $ 109 right parenthesis

equalsnothing

​(Round to four decimal places as​ needed.)

c. What is the probability that the sample mean will be more than

​$113

​?

Upper P left parenthesis x overbar greater than $ 113 right parenthesis

equalsnothing

​(Round to four decimal places as​ needed.)

d. What is the probability that the sample mean will be between

​$106

and

​$108

​?

Upper P left parenthesis $ 106 less than or equals x overbar less than or equals $ 108 right parenthesis

equalsnothing

​(Round to four decimal places as​ needed.)

According to a research​ institution, the average hotel price in a certain year was ​$95.82 . Assume the population standard deviation is ​$18.00 and that a random sample of 36 hotels was selected. Complete parts a through d below. a. Calculate the standard error of the mean. sigma Subscript x overbar equals​$nothing ​(Round to two decimal places as​ needed.) b. What is the probability that the sample mean will be less than ​$98 ​? Upper P left parenthesis x overbar less than $ 98 right parenthesis equalsnothing ​(Round to four decimal places as​ needed.) c. What is the probability that the sample mean will be more than ​$100 ​? Upper P left parenthesis x overbar greater than $ 100 right parenthesis equalsnothing ​(Round to four decimal places as​ needed.) d. What is the probability that the sample mean will be between ​$94 and ​$96 ​? Upper P left parenthesis $ 94 less than or equals x overbar less than or equals $ 96 right parenthesis equalsnothing ​(Round to four decimal places as​ needed.

The average daily rate of a hotel in Canada as of August 2018 was $172.75. Assume the average daily rate follows a normal distribution with a standard deviation of $28.60.

Standard Normal Distribution Table ( note you need access to this table in order to do this question)

a. What is the probability that the average daily rate of a Canadian hotel will be:

(i) less than $175
P(X < 175)=P(X < 175)=

(ii) more than $205
P(X > 205)=P(X > 205)=

(iii) Between $145 and $185
P(145 < X < 185)=P(145 < X < 185)=

b. Determine the average daily rates that separate the:

(i) top 7% of average daily rates from the rest of the daily rates or from the bottom 93% of average daily rates
x=x=

Round to 2 decimal places.

(ii) bottom 25% of average daily rates from the rest of the daily rates
x=x=

Round to 2 decimal places.

(iii) middle 70% of average daily rates from the rest of the daily rates

  < x <  < x <  

Round to 2 decimal places.

h(i,x)=

{10if  program i halts on input x,otherwise.{1if  program i halts on input x,0otherwise.

41. Nancy, the owner of a very successful hotel chain in the Southeast, is exploring the possibility of expanding the chain into a city in the Northeast. She incurs $35,000 of expenses associated with this investigation. Based on the regulatory environment for hotels in the city, she decides not to expand. During the year, she also investigates opening a restaurant that will be part of a national restaurant chain. Her expense for this are $53,000. The restaurant begins operations on September 1. Determine the amount that Nancy can deduct in the current year for investigating these two businesses.

34. Daniel is single and has the following income and expenses in 2017:

Salary income $60,000

Net rent income 6,000

Dividend income 3,500

Payment of alimony 12,000

Mortgage interest on residence 4,900

Property tax on residence 1,200

Contribution to traditional IRA 5,000

Contribution to United Church 2,100

Loss on the sale of real estates (held for investment) 2,000

Medical expenses 3,250

State income tax 300

Federal income tax 7,000

a. Calculate Daniel’s AGI.

b. Should Daniel itemize his deductions from AGI or take the standard deduction? Explain.

Because of staffing decisions, managers of the Gibson-Marimont Hotel are interested in the variability in the number of rooms occupied per day during a particular season of the year. A sample of 24 days of operation shows a sample mean of 294 rooms occupied per day and a sample standard deviation of 26 rooms.

What is the point estimate of the population variance? 676

Provide a 90% confidence interval estimate of the population variance (to 1 decimal). ( , )

Provide a 90% confidence interval estimate of the population standard deviation (to 1 decimal). ( , )