What is the likelihood of the selected flights

Question

Assignment:

Example

Jane is 20 and Joe is 30. What is the sum of their ages? 50 <======= look at the formula in this cell to see how it refers  to the calculated answer below.

Do all of your work below this line. Be sure that each answer cell above refers to the cell in which you have calculated your answer.
age
Jane 20
Joe 30
sum 50

Q1: Refer to the Baseball 2005 data, below, which reports information on the 30 major league teams  for the 2005 baseball season. These data represent a sample of Baseball statistics.

League	Built	Size	Surface	Salary	Salary -mil	Wins	Attendance	Batting	ERA	HR	Error	SB
1	1912	33871	0	123,505,125	123.5	95.0	2,847,798	0.281	4.74	199	109	45
1	1923	57746	0	208,306,817	208.3	95.0	4,090,440	0.276	4.52	229	95	84
1	1966	43662	0	55,425,762	55.4	88.0	2,108,818	0.262	3.69	155	88	31
1	1992	48262	0	73,914,333	73.9	74.0	2,623,904	0.269	4.56	189	107	83
1	1966	45050	0	97,725,322	97.7	95.0	3,404,636	0.270	3.68	147	87	161
1	1994	43368	0	41,502,500	41.5	93.0	2,014,220	0.271	3.61	207	106	62
1	1991	44321	0	75,178,000	75.2	99.0	2,342,804	0.262	3.61	200	94	137
1	1989	50516	1	45,719,500	45.7	80.0	2,014,995	0.265	4.06	136	95	72
1	1982	48678	1	56,186,000	56.2	83.0	2,034,243	0.259	3.71	134	102	102
1	1990	44027	1	29,679,067	29.7	67.0	1,141,915	0.274	5.39	157	124	151
1	1994	52000	0	55,849,000	55.8	79.0	2,525,259	0.267	4.96	260	108	67
1	2000	40000	0	69,092,000	69.1	71.0	2,024,505	0.272	4.51	168	110	66
1	1999	45611	0	87,754,334	87.8	69.0	2,724,859	0.256	4.49	130	86	102
1	1973	40529	0	36,881,000	36.9	56.0	1,371,181	0.263	5.49	126	125	53
0	1993	50062	0	86,457,302	86.5	90.0	2,520,904	0.265	3.98	184	86	92
0	1998	49075	0	62,329,166	62.3	77.0	2,059,327	0.256	4.84	191	94	67
0	2000	42000	0	76,799,000	76.8	89.0	2,805,060	0.256	3.51	161	89	115
0	2003	42,059	0	61,892,583	61.9	73.0	1,923,254	0.261	5.15	222	104	72
0	1964	55775	0	101,305,821	101.3	83.0	2,827,549	0.258	3.76	175	106	153
0	2001	38127	0	38,133,000	38.1	67.0	1,817,245	0.259	4.42	139	117	73
0	1962	56000	0	83,039,000	83.0	71.0	3,603,680	0.253	4.38	149	106	58
0	2004	42,445	0	63,290,833	63.3	82.0	2,869,787	0.257	4.13	130	109	99
0	1961	56000	0	48,581,500	48.6	81.0	2,730,352	0.252	3.87	117	92	45
0	2000	40800	0	90,199,500	90.2	75.0	3,181,020	0.261	4.33	128	90	71
0	1966	49625	0	92,106,833	92.1	100.0	3,542,271	0.270	3.49	170	100	83
0	1987	42531	0	60,408,834	60.4	83.0	1,852,608	0.272	4.16	128	103	96
0	2004	43500	0	95,522,000	95.5	88.0	2,665,304	0.270	4.21	167	90	116
0	2001	42400	0	39,934,833	39.9	81.0	2,211,323	0.259	3.97	175	119	79
0	1914	38957	0	87,032,933	87.0	79.0	3,100,092	0.270	4.19	194	101	65
0	1995	50381	0	48,155,000	48.2	67.0	1,914,385	0.267	5.13	150	118	65

a. Select the variable team salary and find the mean, median, and the standard deviation.

b. Select the variable that refers to the age the stadium was built. (Hint: Subtract the  year in which the stadium was built from the current year to find the stadium age and  work with that variable.) Find the mean, median, and the standard deviation.

c. Select the variable that refers to the seating capacity of the stadium. Find the mean,  median, and the standard deviation.

Q2: Assume the likelihood that any flight on Northwest Airlines arrives within 15 minutes of  the scheduled time is .90. We select four flights from yesterday for study.

a. What is the likelihood all four of the selected flights arrived within 15 minutes of the  scheduled time?

b. What is the likelihood that none of the selected flights arrived within 15 minutes of  the scheduled time?

c. What is the likelihood at least one of the selected flights did not arrive within 15 minutes  of the scheduled time?

Q3: An internal study by the Technology Services department at Lahey Electronics revealed  company employees receive an average of two emails per hour. Assume the arrival of  these emails is approximated by the Poisson distribution.

a. What is the probability Linda Lahey, company president, received exactly 1 email  between 4 P.M. and 5 P.M. yesterday?

b. What is the probability she received 5 or more email during the same period?

c. What is the probability she did not receive any email during the period?

Q4: Fast Service Truck Lines uses the Ford Super Duty F-750 exclusively. Management made  a study of the maintenance costs and determined the number of miles traveled during  the year followed the normal distribution. The mean of the distribution was 60,000 miles  and the standard deviation 2,000 miles.

a. What percent of the Ford Super Duty F-750s logged 65,200 miles or more?

b. What percent of the trucks logged more than 57,060 but less than 58,280 miles?

c. What percent of the Fords traveled 62,000 miles or less during the year?

d. Is it reasonable to conclude that any of the trucks were driven more than 70,000 miles? Explain.

Q5: The mean amount purchased by a typical customer at Churchill's Grocery Store is $23.50  with a standard deviation of $5.00. Assume the distribution of amounts purchased follows  the normal distribution. For a sample of 50 customers, answer the following questions.

a. What is the likelihood the sample mean is at least $25.00?

b. What is the likelihood the sample mean is greater than $22.50 but less than $25.00?

c. Within what limits will 90 percent of the sample means occur?

Q6: Families USA, a monthly magazine that discusses issues related to health and health  costs, surveyed 20 of its subscribers. It found that the annual health insurance premiums  for a family with coverage through an employer averaged $10,979. The standard deviation  of the sample was $1,000.

a. Based on this sample information, develop a 90 percent confidence interval for the  population mean yearly premium. upper lower

b. How large a sample is needed to find the population mean within $250 at 99 percent  confidence? (remember to round to an integer)

Q7: During recent seasons, Major League Baseball has been criticized for the length of the  games. A report indicated that the average game lasts 3 hours and 30 minutes. A sample  of 17 games revealed the following times to completion. (Note that the minutes have  been changed to fractions of hours, so that a game that lasted 2 hours and 24 minutes  is reported at 2.40 hours.)

2.98 2.40 2.70 2.25 3.23 3.17 2.93 3.18 2.80
2.38 3.75 3.20 3.27 2.52 2.58 4.45 2.45

Can we conclude that the mean time for a game is less than 3.50 hours? Use the .05 significance level.

Q8:The amount of income spent on housing is an important component of the cost of living.  The total costs of housing for homeowners might include mortgage payments, property  taxes, and utility costs (water, heat, electricity). An economist selected a sample of  20 homeowners in New England and then calculated these total housing costs as a percent  of monthly income, five years ago and now. The information is reported below. Is it reasonable to conclude the percent is less now than five years ago? Yes No

Home-owner Five Years Ago (%) Now (%) Home-owner Five Years Ago (%) Now (%)
1 17 10 11 35 32
2 20 39 12 16 32
3 29 37 13 23 21
4 43 27 14 33 12
5 36 12 15 44 40
6 43 41 16 44 42
7 45 24 17 28 22
8 19 26 18 29 19
9 49 28 19 39 35
10 49 26 20 22 12

Q9: Martin Motors has in stock three cars of the same make and model. The president would  like to compare the gas consumption of the three cars (labeled car A, car B, and car C)  using four different types of gasoline. For each trial, a gallon of gasoline was added to  an empty tank, and the car was driven until it ran out of gas. The following table shows the number of miles driven in each trial.

Distance (miles)
Types of Gasoline Car A Car B Car C
Regular 22.4 20.8 21.5
Super regular 17.0 19.4 20.7
Unleaded 19.2 20.2 21.2
Premium unleaded 20.3 18.6 20.4

Using the .05 level of significance:

a. Is there a difference among types of gasoline? Yes No

b. Is there a difference in the cars? Yes No

Q10: A regional commuter airline selected a random sample of 25 flights and found that the  correlation between the number of passengers and the total weight, in pounds, of luggage  stored in the luggage compartment is 0.94. Using the .05 significance level, can we  conclude that there is a positive association between the two variables?

Q11: A suburban hotel derives its gross income from its hotel and restaurant operations. The  owners are interested in the relationship between the number of rooms occupied on a  nightly basis and the revenue per day in the restaurant. Below is a sample of 25 days (Monday through Thursday) from last year showing the restaurant income and number of  rooms occupied.

Day Income Occupied Day Income Occupied
1 1,452 23 14 1,425 27
2 1,361 47 15 1,445 34
3 1,426 21 16 1,439 15
4 1,470 39 17 1,348 19
5 1,456 37 18 1,450 38
6 1,430 29 19 1,431 44
7 1,354 23 20 1,446 47
8 1,442 44 21 1,485 43
9 1,394 45 22 1,405 38
10 1,459 16 23 1,461 51
11 1,399 30 24 1,490 61
12 1,458 42 25 1,426 39
13 1,537 54

Use a statistical software package to answer the following questions.

a. Does the breakfast revenue seem to increase as the number of occupied rooms  increases? Draw a scatter diagram to support your conclusion.

b. Determine the coefficient of correlation between the two variables.  Interpret the value.

c. Is it reasonable to conclude that there is a positive relationship between revenue and  occupied rooms? Use the .10 significance level.

d. What percent of the variation in revenue in the restaurant is accounted for by the number  of rooms occupied?

Q12: The district manager of Jasons, a large discount electronics chain, is investigating why  certain stores in her region are performing better than others. She believes that three factors  are related to total sales: the number of competitors in the region, the population in  the surrounding area, and the amount spent on advertising. From her district, consisting  of several hundred stores, she selects a random sample of 30 stores. For each store she  gathered the following information.

Y Total sales last year ($000)
X1 number of competitors in the region
X2 population in the region (in millions)
X3 advertising expense ($000)

The sample data were run on MINITAB, with the following results

Analysis of variance

SOURCE DF SS MS
Regression 3 3050.00 1016.67
Error 26 2200.00 84.62
Total 29 5250.00

Predictor Coef StDev t-ratio
Constant 14.00 7.00 2.00
X1 -1.00 0.70 -1.43
X2 30.00 5.20 5.77
X3 0.20 0.08 2.50

What are the estimated sales for the Bryne store, which has four competitors, a  regional population of 0.4 (400,000), and advertising expense of 30 ($30,000)?

Compute the value.

Compute the multiple standard error of estimate.

Conduct a global test of hypothesis to determine whether any of the regression coefficients  are not equal to zero. Use the .05 level of significance. Are any not equal to zero? Yes

Conduct tests of hypotheses to determine which of the independent variables have  significant regression coefficients. Which variables would you consider eliminating?  Use the .05 significance level.

Q13:Banner Mattress and Furniture Company wishes to study the number of credit applications  received per day for the last 300 days. The information is reported below:

Number of Credit Applications Frequency (Number of Days)
0 50
1 77
2 81
3 48
4 31
5 or more 13

To interpret, there were 50 days on which no credit applications were received, 77 days  on which only one application was received, and so on.

Would it be reasonable to conclude that the population distribution  is Poisson with a mean of 2.0? Yes No Use the .05 significance level.
Hint: To find the expected frequencies use the Poisson distribution with a  mean of 2.0. Find the probability of exactly one success given a Poisson distribution with  a mean of 2.0. Multiply this probability by 300 to find the expected frequency for the  number of days in which there was exactly one application. Determine the expected frequency  for the other days in a similar manner.