suppose we take a die with 3 on three sides 2 on two sides and 1 on one side, roll it n times and let Xi be the number of times side i appeared find the conditional distribution P(X2=k|X3=m)

1. Consider the relationship between the number of bids an item on eBay received and the item's selling price. The following is a sample of 55 items sold through an auction.

Price in Dollars	2222	2626	2727	3636	4545
Number of Bids	11	44	55	55	77

Step 1 of 5: Calculate the sum of squared errors (SSE). Use the values b0= −1.9336 and b1= 0.2030 for the calculations. Round your answer to three decimal places.

Step 2 of 5: Calculate the estimated variance of errors, s2e. Round your answer to three decimal places.

Step 3 of 5: Calculate the estimated variance of slope, s2b1. Round your answer to three decimal places.

Step 4 of 5: Construct the 80% confidence interval for the slope. Round your answers to three decimal places.

Lower endpoint:

Upper endpoint:

Step 5 of 5: Construct the 98% confidence interval for the slope. Round your answers to three decimal places.

Lower endpoint:

Upper endpoint:

Customer	Type of Customer	Items	Net Sales	Method of Payment	Gender	Marital Status	Age
1	Regular	1	49.5	Discover	Male	Married	22
2	Promotional	1	112.4	Proprietary Card	Female	Married	26
3	Regular	1	32.5	Proprietary Card	Female	Married	22
4	Promotional	5	110.4	Proprietary Card	Female	Married	18
5	Regular	2	64	MasterCard	Female	Married	24
6	Regular	1	54.5	MasterCard	Female	Married	34
7	Promotional	2	88	Proprietary Card	Female	Married	20
8	Regular	1	32.5	Visa	Female	Married	30
9	Promotional	2	66.52	Proprietary Card	Female	Married	36
10	Regular	1	54.5	Proprietary Card	Female	Married	26
11	Regular	1	39.5	Proprietary Card	Female	Married	38
12	Promotional	1	41.6	Proprietary Card	Female	Married	30
13	Promotional	9	170.4	Visa	Female	Married	30
14	Promotional	2	74.5	Visa	Female	Married	36
15	Regular	1	59.5	Visa	Male	Single	44
16	Promotional	2	81.4	Proprietary Card	Male	Single	26
17	Promotional	3	104	Proprietary Card	Female	Single	32
18	Regular	3	64.5	Discover	Female	Married	30
19	Promotional	2	48.5	MasterCard	Female	Married	22
20	Promotional	6	54.8	Proprietary Card	Female	Married	46
21	Promotional	1	41.6	Proprietary Card	Female	Single	18
22	Promotional	4	80.82	Proprietary Card	Female	Married	28
23	Promotional	7	276	American Express	Female	Married	40
24	Regular	2	84	Proprietary Card	Female	Married	32
25	Promotional	2	49.5	Visa	Male	Married	38
26	Promotional	1	40.02	Proprietary Card	Female	Married	50
27	Regular	1	54.5	Proprietary Card	Female	Married	44
28	Promotional	5	202.8	Proprietary Card	Female	Single	32
29	Promotional	3	81.2	Proprietary Card	Female	Married	22
30	Promotional	1	28	Proprietary Card	Female	Married	60
31	Promotional	2	73.2	MasterCard	Female	Married	18
32	Regular	1	85	Proprietary Card	Female	Married	42
33	Promotional	3	73.2	Proprietary Card	Female	Married	34
34	Regular	1	50	Proprietary Card	Female	Married	24
35	Promotional	5	115.5	MasterCard	Female	Married	46
36	Regular	1	39.5	MasterCard	Male	Single	26
37	Regular	2	112.5	Visa	Female	Single	32
38	Promotional	6	127.5	Proprietary Card	Female	Married	40
39	Promotional	5	23.23	Proprietary Card	Female	Married	34
40	Regular	2	62.5	Proprietary Card	Female	Married	48
41	Promotional	13	208.8	Proprietary Card	Female	Married	32
42	Promotional	4	29.5	Visa	Female	Married	36
43	Regular	2	133.5	Proprietary Card	Female	Married	38
44	Promotional	1	72.4	Proprietary Card	Female	Married	44
45	Promotional	2	33.8	Proprietary Card	Female	Married	28
46	Promotional	2	49.6	Proprietary Card	Female	Married	50
47	Regular	1	35	MasterCard	Female	Married	36
48	Promotional	3	73.64	Proprietary Card	Female	Married	20
49	Promotional	1	24.82	Proprietary Card	Female	Married	22
50	Promotional	9	155.2	MasterCard	Female	Married	36
51	Promotional	6	186.62	Proprietary Card	Female	Married	28
52	Promotional	5	128.8	Proprietary Card	Male	Married	58
53	Regular	1	68	Discover	Female	Single	68
54	Regular	2	84	Visa	Female	Single	84
55	Regular	2	59.5	MasterCard	Female	Married	22
56	Promotional	3	151.6	Proprietary Card	Female	Married	28
57	Promotional	6	133.1	Proprietary Card	Female	Married	44
58	Promotional	2	90.4	Proprietary Card	Female	Married	38
59	Promotional	4	75.2	MasterCard	Female	Married	36
60	Promotional	4	123	Proprietary Card	Female	Single	40
61	Promotional	1	118.8	Proprietary Card	Female	Married	36
62	Promotional	3	69.91	Proprietary Card	Female	Single	20
63	Promotional	5	63.6	Proprietary Card	Female	Married	44
64	Promotional	1	41.6	Proprietary Card	Female	Single	32
65	Promotional	2	59.5	Proprietary Card	Female	Married	38
66	Promotional	1	49.6	Proprietary Card	Female	Married	52
67	Promotional	2	69.5	Proprietary Card	Female	Married	24
68	Promotional	5	156.8	Proprietary Card	Female	Married	18
69	Promotional	2	57.2	Proprietary Card	Male	Married	36
70	Promotional	8	105.05	Proprietary Card	Female	Married	44
71	Promotional	5	165.32	Proprietary Card	Female	Married	20
72	Promotional	4	68	MasterCard	Female	Married	22
73	Regular	1	79	Proprietary Card	Female	Single	54
74	Promotional	2	56.5	Proprietary Card	Female	Married	22
75	Promotional	2	55.22	Proprietary Card	Female	Married	64
76	Promotional	4	94.74	Proprietary Card	Female	Married	52
77	Regular	2	49	Proprietary Card	Female	Married	32
78	Promotional	4	121.14	Proprietary Card	Female	Married	18
79	Promotional	3	96.8	Proprietary Card	Female	Married	28
80	Regular	2	99	Discover	Female	Married	44
81	Promotional	2	88	MasterCard	Female	Married	58
82	Promotional	6	63.2	Proprietary Card	Female	Single	20
83	Promotional	4	68.5	Visa	Female	Married	26
84	Promotional	3	56	Proprietary Card	Female	Married	34
85	Regular	2	47.5	Visa	Female	Married	34
86	Promotional	1	30.8	Proprietary Card	Female	Married	52
87	Regular	6	154	MasterCard	Female	Single	38
88	Regular	4	117	Proprietary Card	Female	Married	26
89	Promotional	1	41.6	Proprietary Card	Female	Single	50
90	Promotional	6	67.6	Proprietary Card	Female	Married	32
91	Promotional	4	105.2	Proprietary Card	Female	Married	44
92	Promotional	1	32.42	Proprietary Card	Female	Married	44
93	Regular	5	169.75	Proprietary Card	Female	Married	62
94	Promotional	17	239.5	Proprietary Card	Female	Married	20
95	Regular	3	76	American Express	Female	Married	36
96	Regular	1	49.5	MasterCard	Female	Married	34
97	Promotional	9	263	Proprietary Card	Female	Married	20
98	Promotional	10	297.59	Proprietary Card	Female	Married	42
99	Promotional	2	57.6	Proprietary Card	Female	Married	20
100	Promotional	1	38.44	Proprietary Card	Female	Married	34

a) Using the empirical rule, 95% of female promotional customer ages should be between what two values? Either show work or explain how your answer was calculated.

b)Using the empirical rule, 68% of items purchased should be between what two values? Either show work or explain how your answer was calculated.    

1. Consider the table of test scores below:

36	16	61	97	27
37	64	59	91	81
86	39	56	85	26
36	51	18	68	69
78	61	49	29	82

1. Find the Mean.
2. Find the Median.
3. Find the Mode.
4. Discuss which of these statistics you would use to describe this set of test scores and back up your choice with some reasoning from the book or from your notes.

Consider the following experiment: we roll a fair die twice. The two rolls are independent events. Let’s call M the number of dots in the first roll and N the number of dots in the second roll.

(a) What is the probability that both M and N are even?

(b) What is the probability that M + N is even?

(c) What is the probability that M + N = 5?

(d) We know that M + N = 5. What is the probability that M is an odd number?

(e) We know that M is an odd number. What is the probability that M + N = 5?

A company maintains three offices in a certain region, each staffed by two employees. Information concerning yearly salaries (1000s of dollars) is as follows:

Office	1	1	2	2	3	3
Employee	1	2	3	4	5	6
Salary	24.7	28.6	25.2	28.6	20.8	24.7

(a) Suppose two of these employees are randomly selected from among the six (without replacement). Determine the sampling distribution of the sample mean salary X. (Enter your answers for p(x) as fractions.)

x	22.75		24.70	24.95	26.65		28.60
p(x)		1 15				2 15

(b) Suppose one of the three offices is randomly selected. Let X₁ and X₂ denote the salaries of the two employees. Determine the sampling distribution of X. (Enter your answers as fractions.)

x	22.75	26.65	26.90
p(x)

(c) How does E(X) from parts (a) and (b) compare to the population mean salary μ?

E(X) from part (a) is  _______ μ, and E(X) from part (b) is _______ μ.

The following table shows the length of stay distribution for guests staying at a beach resort, in days. The resort management makes a net profit of $250 per day per guest during the first 2 days of the stay, and $150 per day per guest after the first 2 days. How much profit will the resort owners make in a month (assuming 30 days in a month) if there are 100 guests arriving per day? [Hint: Note that a guest who only stays for two days is billed $500; find the average profit for one guest then work out for the entire month.]

Must be completed in Excel

Days	2	3	4	5	6	7	8	9	10
Prob (%)	5	10	12	12	11	15	14	12	9

Fill in the blank. In a drive thru performance study, the average service time for McDonald's is 203.21 seconds with a standard deviation of 5.67 seconds. A random sample of 90 times is taken. There is a 51% chance that the average drive-thru service time is less than ________ seconds.

1)

203.22

2)	There is not enough information to determine this.

3)

203.2

4)

203.07

5)

203.35

Men at a construction site were moving concrete blocks from a truck, a short distance to the base of a house. The first day the average man moved 62 blocks per hour.

The current day the numbers were : 70,63,76,86,86,62,97,70,77,81

1. Assume all assumptions are met. Provide descriptive statistics for the sample.

2. Conduct a statistical test to assess if the men were able to move more than 62 blocks per hour.

3. The men had more rest than they did the first day and were certain they could move atleast 5 more blocks per hour. Conduct a statistical test to see if they were able to, on average, move 5 more plants per hour than the previous mark of 62

A. Here is a bivariate data set.

x	y
25.7	52.5
29.4	64.7
21.8	54.9
35	63.4
31.4	74.7
21.6	46.5
40.8	69.7
37.9	77.7
16.7	41.1
29.6	78.1
13.1	45.5
36.1	78.4
32.1	68.2
45.2	76.8
36.1	57.9

Find the correlation coefficient and report it accurate to three decimal places.
r =
What proportion of the variation in y can be explained by the variation in the values of x? Report answer as a percentage accurate to one decimal place.
r² = %

B. Based on the data shown below, calculate the correlation coefficient (to three decimal places)

x	y
1	4.97
2	4.04
3	3.51
4	3.78
5	5.15
6	7.22
7	6.69
8	5.76
9	6.73
10	6.6
11	9.77
12	8.24
13	6.91

A claim with an alpha =0.10 and a mu of 20. A sample size of 30 yields a sample mean of 17.5 and a sample standard deviation of 10. What is the upper confidence limit with 3 decimal places?

Distillation is a process for separating and collecting substances according to their reaction to heat. When heat is applied to a mixture, the substance that evaporates and is collected as it cools is the distillate. The unevaporated portion of the mixture is the residue. Oil obtained from orange blossoms through distillation is used in perfume. Suppose the oil yield is normally distributed. In a random sample of eleven distillations, the sample mean oil yield was 980.2 grams with sample standard deviation 27.6 grams. If possible, answer (a) to (d). If not possible, explain.

(a) Find the point estimate.

(b) Find the standard error.

(c) Find the margin of error at the 99% confidence level.

(d) Find and interpret the 99% confidence interval.

Let x = age in years of a rural Quebec woman at the time of her first marriage. In the year 1941, the population variance of x was approximately σ² = 5.1. Suppose a recent study of age at first marriage for a random sample of 51 women in rural Quebec gave a sample variance s² = 3.0. Use a 5% level of significance to test the claim that the current variance is less than 5.1. Find a 90% confidence interval for the population variance. (a) What is the level of significance?


State the null and alternate hypotheses.

H_o: σ² = 5.1; H₁: σ² ≠ 5.1

H_o: σ² = 5.1; H₁: σ² > 5.1    

H_o: σ² < 5.1; H₁: σ² = 5.1

H_o: σ² = 5.1; H₁: σ² < 5.1

(b) Find the value of the chi-square statistic for the sample. (Round your answer to two decimal places.)


What are the degrees of freedom?


What assumptions are you making about the original distribution?

We assume a normal population distribution.

We assume a uniform population distribution.    

We assume a binomial population distribution.

We assume a exponential population distribution.

(c) Find or estimate the P-value of the sample test statistic.

P-value > 0.100

0.050 < P-value < 0.100    

0.025 < P-value < 0.050

0.010 < P-value < 0.025

0.005 < P-value < 0.010

P-value < 0.005

(d) Based on your answers in parts (a) to (c), will you reject or fail to reject the null hypothesis?

Since the P-value > α, we fail to reject the null hypothesis. Since the P-value > α, we reject the null hypothesis.     Since the P-value ≤ α, we reject the null hypothesis. Since the P-value ≤ α, we fail to reject the null hypothesis.

(e) Interpret your conclusion in the context of the application.

At the 5% level of significance, there is insufficient evidence to conclude that the variance of age at first marriage is less than 5.1.

At the 5% level of significance, there is sufficient evidence to conclude that the that the variance of age at first marriage is less than 5.1.    

(f) Find the requested confidence interval for the population variance. (Round your answers to two decimal places.)

lower limit
upper limit

Interpret the results in the context of the application.

We are 90% confident that σ² lies outside this interval.

We are 90% confident that σ² lies below this interval.    

We are 90% confident that σ² lies within this interval.

We are 90% confident that σ² lies above this interval.

0-499	22
500-999	201
1000-1499	1,645
1500-1999	9,365
2000-2499	92,191
2500-2999	569,319
3000-3499	1,387,335
3500-3999	988,011
4000-4499	255,700
4500-4999	36,766
5000-5499	3,994

0-499	22
500-999	201
1000-1499	1,645
1500-1999	9,365
2000-2499	92,191
2500-2999	569,319
3000-3499	1,387,335
3500-3999	988,011
4000-4499	255,700
4500-4999	36,766
5000-5499	3,994

D) Use the normal model to determine the proportion of babies in each class

How do I manually determine the normal mode? Please provide step by step manually (excel is what I am using, however I need to show steps.

Thank you.