Based on annual driving of 15,000 miles and fuel efficiency of 20 mpg, a car in the United States uses, on average, 700 gallons of gasoline per year. If annual automobile fuel usage is normally distributed, and if 26.76% of cars in the United States use less than 480 gallons of gasoline per year, what is the standard deviation?

Round your answer to 2 decimal places, the tolerance is +/-0.05.

Suppose that nn independent trials are performed, with trial ii being a success with probability 1/(2i+1).12i1. Let PnPndenote the probability that the total number of successes that result is an odd number.

1.Find Pn for n=1,2,3,4,5.

2.Conjecture a general formula for Pn.

3. Derive a formula for Pn in terms of Pn−1

Verify that your conjecture in part (b) satisfies the recursive formula in part (c). Because the recursive formula has a unique solution, this then proves that your conjecture is correct.

The manufacturer of a portable music player (PMP) has shown that the average life of the product is 72 months with a standard deviation of 12 months. The manufacturer is considering using a new parts supplier for th PMP's and want to test that the new hard drives will increase the life of the PMP. Before manufacturing the PMP's on a lareg scale, the manufactuer sampled 200 PMP's and found the average life to be 78 months. Test the hypothesis using alpha = .01 that the new hard drives will increase the life of the PMP's. Assume the standard deviation of the new PMP's is the same as the standard deviation of the older model.

A website developer has indicated to potential clients that for the sites he has developed visitors spend an average of 45 minutes per day on the sites. One of his potential clients conducted a survey of 20 visitors to several of his sites and found that the average time spent was 35 minutes with a standard deviation of 7 minutes. Determine if there is sufficient evidence to conclude that the average time spent on the sites is different from what he indicated. Conduct the test at the 0.05 level.

In both cases, in addition to testing the hypotheses using a critical value, also calculate the p value for the test statistic.

A random sample of 43 taxpayers claimed an average of $9,853 in medical expenses for the year. Assume the population standard deviation for these deductions was ​2,418. Construct confidence intervals to estimate the average deduction for the population with the levels of significance shown below.

a.1%

b.5%

c.20%

a. The confidence interval with a 1% level of significance has a lower limit of _____ and an upper limit of ______.

b. The confidence interval with a 5% level of significance has a lower limit of _____ and an upper limit of ______.

c. The confidence interval with a 20% level of significance has a lower limit of _____ and an upper limit of ______.

In looking at our class’s data as a sample of a larger population of students (who have taken, are taking, or may one day take this class), we find that the mean number of hours exercised per week during the summer is nearly 9 hours. We know that this is an estimate however. Is it likely that the true population mean is actually under 7 hours? Use a 95% confidence interval to determine this. If we’re willing to use a 99% confidence interval, does that change our findings? (Careful with your rounding!)

. mean exersum

Mean estimation                   Number of obs   =        215

--------------------------------------------------------------

             |       Mean   Std. Err.     [95% Conf. Interval]

-------------+------------------------------------------------

     exersum |   8.946512   .7143183     

Upon reviewing recent use of conference rooms at an engineering consulting firm, an industrial engineer determined the following probability distribution for the number of requests for a conference room per half-day: X 0 1 2 3 4 P(X=x) 0.07 0.15 0.45 0.25 0.08 a) Is this a legitimate probability distribution function? b) Currently, the building has two conference rooms. What is the probability that the number of requests will exceed the number of rooms for a given half-day? c) What is the probability that the two conference rooms will not be fully utilized on a given half-day? d) Obtain the mean, the standard deviation for the number of requests for conference rooms. e) Draw a probability histogram

For given list of members in a universal set U.

Members A B

1 a1 b1

2 a2 b1

3 a3 b2

4 a1 b2

5 a1 b2

6 a2 b1

7 a3 b1

8 a1 b2

9 a1 b2

10 a3 b2

Write Probability distribution table for

(a) P(A, B)

(b) P(A)

(c) P(B)

(d) P(A|B=b1)

A small independent physicians' practice has three doctors. Dr. Sarabia sees 41% of the patients, Dr. Tran sees 32% , and Dr. Jackson sees the rest. Dr. Sarabia requests blood tests on 5% of her patients, Dr. Tran requests blood tests on 8% of his patients, and Dr. Jackson requests blood tests on 6% of her patients. An auditor randomly selects a patient from the past week and discovers that the patient had a blood test as a result of the physician visit. Knowing this information, what is the probability that the patient saw Dr. Sarabia? For what percentage of all patients at this practice are blood tests requested?

(Round your answer to 4 decimal places.)

p = ______________

(enter the probability that a randomly selected patient was seen by Dr. Sarabia last week rounded to 4 decimal places)

For what percentage of all patients at this practice are blood tests requested?

(Round your answer to 2 decimal places.)

p = _______________

(enter the share of all the patients for which blood tests are requested in percentages rounded to 2 decimal places  %)

  In games of the KENO or LOTTO style, the bettor selects numbers from a fixed set. Then the game operator selects another set of numbers, and the bettor wins according to the number of matches.   

a.​Suppose that the game uses the numbers 1 through 50, and suppose that the operator selects eight of these. If the bettor selects five numbers, find the probability that there are exactly five matches. HINT: Think Hypergeometric

b.​Suppose that the game uses the numbers 1 through 50, and suppose that the operator selects ten of these. If the bettor selects five numbers, find the probability that there are exactly five matches. Also note whether this probability is larger or smaller than the probability in a.   

c.​Suppose that the game uses the numbers 1 through 50, and suppose that the operator selects ten of these. If the bettor selects six numbers, find the probability that there are exactly six matches. Note whether the probability here is larger or smaller than the probability in b.

Diameters of 30 rivet heads in 1/100 of an inch are given below:

1. Prepare a Stem-and-leaf plot of the sample, and comment.
2. What is the modal diameter of the rivets?
3. Calculate coefficient of skewness, and comment on it.
4. Find Q1, Q2, and Q3.
5. Find 93^rd percentile and interpret this value.
6. Draw a box plot and comment.
7. Do the data satisfy Empirical Rule?
8. Calculate coefficient of variation and comment on it. Is the variation in the sample relative to the mean too much?
1. Prepare a relative frequency distribution of the data.
10. What proportion of the observations that fall below the first quartile for the above sample?
11. What proportion of the observations that fall above the mean?
50. What proportion of the observations that fall within 2 standard deviation of the mean?
1000. Calculate z-scores of the smallest and the largest observations in the sample. What do they add?

1. There are two machines available for cutting corks intended

for use in wine bottles. The first produces corks with diameters

that are normally distributed with mean 3 cm and standard

deviation .1 cm. The second machine produces corks

with diameters that have a normal distribution with mean

3.04 cm and standard deviation .02 cm. Acceptable corks

have diameters between 2.9 cm and 3.1 cm. Which machine

is more likely to produce an acceptable cork?

2. The weight distribution of parcels sent in a certain manner

is normal with mean value 12 lb and standard deviation

3.5 lb. The parcel service wishes to establish a weight value

c beyond which there will be a surcharge. What value of c

is such that 99% of all parcels are at least 1 lb under the surcharge

weight?

9. Let X denote the distance (m) that an animal moves from its

birth site to the first territorial vacancy it encounters.

Suppose that for banner-tailed kangaroo rats, X has an exponential

distribution with parameter lamda=.01386 (as suggested

in the article “Competition and Dispersal from

Multiple Nests,” Ecology, 1997: 873–883). What is the probability that the distance is at most

100 m? At most 200 m? Between 100 and 200 m?

10. Find the z value to the right of the mean so that

a. 54.78% of the area under the distribution curve lies

to the left of it.

b. 69.85% of the area under the distribution curve lies

to the left of it.

c. 88.10% of the area under the distribution curve lies

to the left of it.

11. The average annual salary for all

U.S. teachers is $47,750. Assume that the distribution is

normal and the standard deviation is $5680. Find the

probability that a randomly selected teacher earns

a. Between $35,000 and $45,000 a year

b. More than $40,000 a year

c. If you were applying for a teaching position and

were offered $31,000 a year, how would you feel

(based on this information)?

12.The national average SAT score (for

Verbal and Math) is 1028. If we assume a normal

distribution with standard deviation 92, what is the 90th percentile

score? What is the probability that a randomly selected

score exceeds 1200?

13. The average credit card debt for

college seniors is $3262. If the debt is normally

distributed with a standard deviation of $1100, find

these probabilities.

a. That the senior owes at least $1000

b. That the senior owes more than $4000

c. That the senior owes between $3000 and $4000

14. The average waiting time to be

seated for dinner at a popular restaurant is 23.5 minutes,

with a standard deviation of 3.6 minutes. Assume the

variable is normally distributed. When a patron arrives

at the restaurant for dinner, find the probability that the

patron will have to wait the following time.

a. Between 15 and 22 minutes

b. Less than 18 minutes or more than 25 minutes

c. Is it likely that a person will be seated in less than

15 minutes?

1. Calculate and interpret the three aspects of Descriptive Analysis for weekly return: Location, Shape and Spread. Hint: make sure you interpret these measures in the context of the data and pay attention to the unit of measurement in Excel.

2. Date	Weekly Return BIT
   11/3/13	-46.16
   18/3/13	-0.01
   25/3/13	39.23
   1/4/13	13.07
   8/4/13	23.93
   15/4/13	41.36
   22/4/13	26.5
   29/4/13	20.39
   6/5/13	25.5
   13/5/13	42.52
   20/5/13	37.88001
   27/5/13	15.66
   3/6/13	20.98
   10/6/13	25.28
   17/6/13	11.97
   24/6/13	-2.46
   1/7/13	14.95
   8/7/13	-3.5
   15/7/13	-8
   22/7/13	-0.05
   29/7/13	25.49
   5/8/13	4.099998
   12/8/13	9.529999
   19/8/13	58.75
   26/8/13	36.12
   2/9/13	47.87
   9/9/13	43.09
   16/9/13	42.08
   23/9/13	40.24001
   30/9/13	51.77
   7/10/13	93.52
   14/10/13	113.89
   21/10/13	133.5
   28/10/13	231.05
   4/11/13	447.08
   11/11/13	874.55
   18/11/13	1091.99
   25/11/13	916.27
   2/12/13	927.8199
   9/12/13	681.78
   16/12/13	789.11
   23/12/13	899
   30/12/13	937.92
   6/1/14	877.1
   13/1/14	900
   20/1/14	828.99
   27/1/14	750
   3/2/14	640
   10/2/14	628.37
   17/2/14	550
   24/2/14	574.73
   3/3/14	569.53
   10/3/14	546.83
   17/3/14	460
   24/3/14	418.31
   31/3/14	375
   7/4/14	467.54
   14/4/14	369
   21/4/14	402.16
   28/4/14	356
   5/5/14	410.9
   12/5/14	548.66
   19/5/14	652.71
   26/5/14	650
   2/6/14	571.71
   9/6/14	590
   16/6/14	565
   23/6/14	561.2
   30/6/14	592.14
   7/7/14	514.12
   14/7/14	500.84
   21/7/14	565.93
   28/7/14	587.76
   4/8/14	484.97
   11/8/14	443
   18/8/14	410.53
   25/8/14	437.92
   1/9/14	462.43
   8/9/14	324.44
   15/9/14	360.15
   22/9/14	253.36
   29/9/14	381.64
   6/10/14	385.55
   13/10/14	349.98
   20/10/14	319.9
   27/10/14	340.98
   3/11/14	363.96
   10/11/14	348.09
   17/11/14	371.5
   24/11/14	376
   1/12/14	319.55
   8/12/14	334.97
   15/12/14	343.46
   22/12/14	262.8
   29/12/14	250.09
   5/1/15	190.02
   12/1/15	380.51
   19/1/15	189.48
   26/1/15	209.59
   2/2/15	223.9
   9/2/15	223.5
   16/2/15	254.85
   23/2/15	251.34
   2/3/15	305.86
   9/3/15	249.82
   16/3/15	280
   23/3/15	220.56
   30/3/15	279.94
   6/4/15	265
   13/4/15	200
   20/4/15	224.68
   27/4/15	195.91
   4/5/15	245.03
   11/5/15	227.36
   18/5/15	269.69
   25/5/15	228.8
   1/6/15	220.5
   8/6/15	212.87
   15/6/15	225.62
   22/6/15	262.18
   29/6/15	343.58
   6/7/15	312.15
   13/7/15	301.96
   20/7/15	315
   27/7/15	262.04
   3/8/15	229.08
   10/8/15	257.53
   17/8/15	220.4
   24/8/15	249.46
   31/8/15	230.8
   7/9/15	223.27
   14/9/15	246.48
   21/9/15	250.66
   28/9/15	239.59
   5/10/15	273.53
   12/10/15	300.01
   19/10/15	377.69
   26/10/15	451.39
   2/11/15	371.79
   9/11/15	376.89
   16/11/15	418.39
   23/11/15	440.58
   30/11/15	505.46
   7/12/15	516.24
   14/12/15	481.21
   21/12/15	482.38
   28/12/15	542.2
   4/1/16	454.28
   11/1/16	473.92
   18/1/16	432.58
   25/1/16	429.39
   1/2/16	467.05
   8/2/16	509.61
   15/2/16	506.68
   22/2/16	448.07
   29/2/16	443.69
   7/3/16	484.58
   14/3/16	489.97
   21/3/16	485.82
   28/3/16	455.66
   4/4/16	474.93
   11/4/16	516.19
   18/4/16	488.28
   25/4/16	555.87
   2/5/16	542.67
   9/5/16	512.75
   16/5/16	601.27
   23/5/16	688.69
   30/5/16	803.09
   6/6/16	953.05
   13/6/16	805.65
   20/6/16	797.08
   27/6/16	771.54
   4/7/16	795.01
   11/7/16	793.52
   18/7/16	723.18
   25/7/16	687.93
   1/8/16	650.5
   8/8/16	660
   15/8/16	670
   22/8/16	715.6
   29/8/16	714
   5/9/16	734.99
   12/9/16	686.2
   19/9/16	719.42
   26/9/16	715.57
   3/10/16	754
   10/10/16	761.02
   17/10/16	825
   24/10/16	825.83
   31/10/16	831.9
   7/11/16	900.52
   14/11/16	902.97
   21/11/16	924.27
   28/11/16	975.2
   5/12/16	1006.2
   12/12/16	1135.94
   19/12/16	1281.4
   26/12/16	1144.41
   2/1/17	995.16
   9/1/17	1123.2
   16/1/17	1138.34
   23/1/17	1247.74
   30/1/17	1241.48
   6/2/17	1275.95
   13/2/17	1453.46
   20/2/17	1590.27
   27/2/17	1549.1
   6/3/17	1262.27
   13/3/17	1177.61
   20/3/17	1372.88
   27/3/17	1512.83
   3/4/17	1488.75
   10/4/17	1583.46
   17/4/17	1681.71
   24/4/17	2096.67
   1/5/17	2495.07
   8/5/17	2760.85
   15/5/17	2994.79
   22/5/17	3393.27
   29/5/17	3789.46
   5/6/17	3488.86
   12/6/17	3403.31
   19/6/17	3242.76
   26/6/17	3315.51
   3/7/17	2410
   10/7/17	3441.5
   17/7/17	3429.74
   24/7/17	3960.53
   31/7/17	5218.14
   7/8/17	5198.76
   14/8/17	5520
   21/8/17	5918.4
   28/8/17	5219.46
   4/9/17	4493.05
   11/9/17	4525.38
   18/9/17	5465.36
   25/9/17	5787.35
   2/10/17	7126.76
   9/10/17	7613.93
   16/10/17	7918.65
   23/10/17	9592.39
   30/10/17	7824.89
   6/11/17	10593.55
   13/11/17	12197.99
   20/11/17	14924.19
   27/11/17	21084.87
   4/12/17	25886.55
   11/12/17	18839.79
   18/12/17	18950.74
   25/12/17	22762.21
   1/1/18	18941.51
   8/1/18	15048.37
   15/1/18	14345.12
   22/1/18	10125.82
   29/1/18	10282.72
   5/2/18	13238.45
   12/2/18	12200.72
   19/2/18	14663.94
   26/2/18	12043.73
   5/3/18	10546.88
   12/3/18	10939.19
   19/3/18	8735.98
   26/3/18	9030.39
   2/4/18	10554.32
   9/4/18	11257.21
   16/4/18	12332.76
   23/4/18	12582.62
   30/4/18	11460.03
   7/5/18	11218.46
   14/5/18	9652.02
   21/5/18	10133.1
   28/5/18	8856.31
   4/6/18	8617.19
   11/6/18	8152.91
   18/6/18	8389.05
   25/6/18	8853.63
   2/7/18	8455.52
   9/7/18	9847.28
   16/7/18	11014.06
   23/7/18	9459.81
   30/7/18	8619.77
   6/8/18	8820.44
   13/8/18	9072.49
   20/8/18	9981.22
   27/8/18	8702.43
   3/9/18	8958.83
   10/9/18	9018.22
   17/9/18	9039.68
   24/9/18	9164.69
   1/10/18	8635.74
   8/10/18	8905.48
   15/10/18	8919.61
   22/10/18	8808.97
   29/10/18	8741.39
   5/11/18	7479.24
   12/11/18	5335.57
   19/11/18	5486.65
   26/11/18	4814.89
   3/12/18	4340.44
   10/12/18	5496.18
   17/12/18	5356.26
   24/12/18	5586.6
   31/12/18	4808.14
   7/1/19	4862.34
   14/1/19	4842.09
   21/1/19	4634.24
   28/1/19	5032.33
   4/2/19	4983.2
   11/2/19	5113.99
   18/2/19	5240.09
   25/2/19	5455.14
   4/3/19	5526.45
   11/3/19	5517.53
   18/3/19	5638.09
   25/3/19	7153.71
   1/4/19	7114.66
   8/4/19	7337.26
   15/4/19	7305.25
   22/4/19	8020.41
   29/4/19	9862.31
   6/5/19	11784.94
   13/5/19	12517.35
   20/5/19	12506.94
   27/5/19	10883.83
   3/6/19	12861.26
   10/6/19	15472.87
   17/6/19	15080.16
   24/6/19	16268.05
   1/7/19	14557.08
   8/7/19	14957.73
   15/7/19	13791.59
   22/7/19	16032.89
   29/7/19	16937.56
   5/8/19	15248.79
   12/8/19

An investment advisor claimed that BIT return is 2%. Do you agree? Justify your reasoning using a two-tailed hypothesis test approach at the significance level of 5% in Excel.

The article "College Graduates Break Even by Age 33" reported that 5.7% of high school graduates were unemployed in 2008 and 9.7% of high school graduates were unemployed in 2009.† Suppose that the reported percentages were based on independently selected representative samples of 300 high school graduates in each of these two years.

(a)Construct a 99% confidence interval for the difference in the proportion of high school graduates who were unemployed in these two years. (Use p2008 − p2009. Round your answers to three decimal places.)

B) The same article reported that 2.6% of college graduates were unemployed in 2008 and 4.6% of college graduates were unemployed in 2009. Suppose that the reported percentages were based on independently selected representative samples of 500 college graduates in each of these two years. A 95% confidence interval for the difference in the proportion of college graduates who were unemployed in these two years was calculated to be (−0.043, 0.003). Is the confidence interval from part (a) wider or narrower than this confidence interval? (Round your answers to three decimal places.)The width of the confidence interval in part (a) is _______ and the width of the given confidence interval is _________ . Thus, the confidence interval in part (a) is