The closing stock price of Ahmadi, Inc. is normally distributed with a mean of 220 dollars and a standard deviation of 20 dollars.

find:

a.The probability of a closing stock price greater than 241.25 dollars is

b.The probability of a closing stock price less than 250 dollars is

c.What percent of closing stock prices are between 180 and 220 dollars?

d.What is the minimum closing stock price of the middle 90% of the closing prices?

Your company manufactures audio tapes for machinery markets. The thickness of the magnetic coating is an important characteristic. Random samples of size 4 are selected, and the thickness is measured using an optical instrument. Table 1 shows the mean and standard deviation for 25 samples. The specifications of its design are 38.0 ± 4.5 mm. If a coating thickness is less than the specifications call for, that tape can be used for a different purpose by running it through another coating operation.

A. Find the trial central line and control limits for the S-chart.

B. Find the trial central line and control limits for the X- bar chart.

C. Assuming the thickness of the coating to be normally distributed, what proportion of the product will not meet specifications?

D. Find the process capability indices of Cp, CPU, CPL, and Cpk.

Please show your work and Explain

Use R studio.

Bacteria in water are counted as colony-forming units (CFU’s) per milliliter.  Ten bottles of water are randomly selected for sampling, with the intention of testing if two different labs produce the same results. Each bottle is divided into two parts, and then given to each of the two labs:

1. Are the ten observations from lab 1 independent of those from lab 2? Why or why not?

Test the hypothesis that the average value from lab 1 higher than that of lab two (a = 0.05). Hint: you can read the data in as vectors, e.g.:

lab1 = c(875,959,475,589,925,1100,971,450,892,728)

2. What are the null and alternative hypotheses?
3. What is the test statistic and its p-value?
4. What decision and conclusion should you make?

Use R studio

1. As of March 23, 2020, the number of COVID19 cases in the state of Florida was 1007, with 13 deaths. The number of cases in Louisiana was 837, with 20 deaths. We are interested in comparing the state’s mortality rates.  
   1. Construct a 95% confidence intervals for the difference of the two unknown population proportions. Draw some conclusions.
   2. Test the hypothesis that the state of Louisiana has a higher mortality rate at a = 0.1.
      1. What are the null and alternative hypotheses?
      2. What is the test statistic, and p-value?
      3. What decision and conclusion should you make?
   3. Would we get a different answer using a = 0.05?

3. A psychologist wants to determine the effect of instructions on the time required to solve a mechanical puzzle. Each of 20 volunteers is given the same mechanical puzzle to be solved as rapidly as possible. Before the task, the subjects are randomly assigned in equal numbers to receive two different sets of instructions. One group is told that their task is difficult (M₁), and the other group is told that their task is easy (M₂). The score for each subject reflects the time in minutes required to solve the puzzle. Use a t-test to evaluate the null hypothesis at the .05 level of significance.

                                     Solution Times

"Difficult" Task                                            "Easy" Task

5                                                                     13

20                                                                    6

7                                                                     6

23                                                                    5

30                                                                    3

24                                                                    6

9                                                                     10

8                                                                     20

20                                                                    9

12                                                                    12

___                                                                  ____

A psychologist conducted a survey of the attitude towards the sustainability of American energy consumption with 230 randomly selected individuals several years ago. The psychologist believes that these attitudes have changed over time. To test this he randomly selects 230 individuals and asks them the same questions. Can the psychologist confirm his theory that the attitudes have changed from the first survey to the second survey? Attitude 1st Survey 2nd Survey Optimistic 35% ,38% Slightly Optimistic 12% ,14% Slightly Pessimistic 9%, 4% Pessimistic 44% ,44%

Step 8 of 10 : Find the critical value of the test at the 0.01 level of significance. Round your answer to three decimal places.

At Spring Break, you decide to take what you have learned in Business Statistics and apply it in Las Vegas. You hit the roulette table and you bet on red each time. The probability of winning is approximately 0.47. You bet on red 5 times. Calculate the probability of losing at least 2 times. (Use Binomial Distribution)

Does the amount of hazardous material absorbed by the bodies of hazardous waste workers depend on gender? You want to test the hypotheses that the amount absorbed by men (group 1) is different from the amount absorbed by women (group 2). A random sample of 212 male workers and 114 female workers showed an average lead absorption in the blood of 12.59 (SD = 1.897) and 12.75 (SD = 0.621), respectively (measured in micrograms/deciliter). Assuming that the population standard deviations are the same, perform a two independent samples t-test on the hypotheses Null Hypothesis: μ1 = μ2, Alternative Hypothesis: μ1 ≠ μ2. What is the test statistic and p-value of this test?

Question 14 options: 1) Test Statistic: -0.875, P-Value: 1.8089

2) Test Statistic: -0.875, P-Value: 0.3822

3) Test Statistic: -0.875, P-Value: 0.1911

4) Test Statistic: -0.875, P-Value: 0.8089

5) Test Statistic: 0.875, P-Value: 0.3822

130 adults with gum disease were asked the number of times per week they used to floss before their diagnoses. The (incomplete) results are shown below:

a. Complete the table (Use 4 decimal places when applicable)

b. What is the cumulative relative frequency for flossing 6 times per week? %

250 people are asked how many siblings they have?

a. Complete the table (Use 4 decimal places when applicable)

b. What percent of the people have exactly one sibling? %

50 part-time students were asked how many courses they were taking this term. The (incomplete) results are shown below:

a. Complete the table.

b. What percent of students take exactly one course? %

50 part-time students were asked how many courses they were taking this term. The (incomplete) results are shown below:

Please fill out the table.

What percent of students take exactly two courses? %

A hospital director is told that 55% of the treated patients are insured. The director wants to test the claim that the percentage of insured patients is less than the expected percentage. A sample of 240 patients found that 120 were insured. At the 0.05 level, is there enough evidence to support the director's claim?

1.Which of the following statements is not true about the level of significance in a hypothesis test?

A.The larger the level of significance, the more likely you are to reject the null hypothesis

B.The level of significance is the maximum risk we are willing to accept in making a Type II error

C.The significance level determines the total size of the rejection region(s)

D.The level of significance provides the critical value(s) of the hypothesis test

2.If an economist wishes to determine whether there is evidence that average family income in a community equals $25,000

A.either a one-tailed or two-tailed test could be used with equivalent results

B.a lower-tailed test should be utilized

C.an upper-tailed test should be utilized

D.a two-tailed test should be utilized

3.If the level of significance of a hypothesis test is raised from 0.01 to 0.05, the probability of a Type II error

A.will also increase from 0.01 to 0.05

B.will decrease

C.will not change

D.will increase

4.The president of a university would like to estimate the proportion of the student population who owns a personal computer. In a sample of 500 students, 417 own a personal computer. Which one of the following statements is false?

A.None of these is false

B. A 90% confidence interval calculated from the same data would be narrower than a 99% confidence interval

C. The parameter of interest is the proportion of the student population who own a personal computer

D.It is possible that the 99% confidence interval calculated from the data will not contain the proportion of the student population who own a personal computer

A large furniture company claims that 65% of all individuals who buy chairs from its stores choose wood chairs, 20% choose plastic chairs, and 15% choose metal chairs. To investigate this claim, researchers collected data from a random sample of the company's customers. The results were 305 wood, 121 plastic, and 74 metal. Are the data from the sample consistent with the company's claim? Conduct an appropriate statistical test at the 5% significance level to support your conclusion. Make sure to include parameters, check conditions, and show calculations before formulating a conclusion. (10 points)

The director of admissions of a small college selected 120 students at random from the new freshman class in a study to determine whether a student’s grade point average (GPA) at the end of the freshman year (y) can be predicted from the ACT test score (x1).

GPA ACT ITS RP   
3.897 21 122 99
3.885 14 132 71
3.778 28 119 95
2.540 22 99 75
3.028 21 131 46
3.865 31 139 77
2.962 32 113 85
3.961 27 136 99
0.500 29 75 13
3.178 26 106 97
3.310 24 125 69
3.538 30 142 99
3.083 24 120 97
3.013 24 107 55
3.245 33 125 93
2.963 27 121 80
3.522 25 119 63
3.013 31 128 78
2.947 25 106 93
2.118 20 123 22
2.563 24 111 84
3.357 21 113 87
3.731 28 134 98
3.925 27 128 95
3.556 28 126 63
3.101 26 121 79
2.420 28 104 86
2.579 22 113 90
3.871 26 133 97
3.060 21 125 39
3.927 25 128 97
2.375 16 112 57
2.929 28 107 67
3.375 26 115 81
2.857 22 119 75
3.072 24 113 63
3.381 21 115 15
3.290 30 110 95
3.549 27 122 93
3.646 26 118 99
2.978 26 114 90
2.654 30 112 99
2.540 24 106 85
2.250 26 95 84
2.069 29 102 58
2.617 24 114 86
2.183 31 116 82
2.000 15 93 34
2.952 19 120 34
3.806 18 117 23
2.871 27 119 95
3.352 16 115 41
3.305 27 113 28
2.952 26 108 68
3.547 24 116 54
3.691 30 135 77
3.160 21 108 58
2.194 20 110 73
3.323 30 124 94
3.936 29 130 98
2.922 25 118 99
2.716 23 110 91
3.370 25 117 95
3.606 23 123 72
2.642 30 116 65
2.452 21 109 53
2.655 24 110 81
3.714 32 126 41
1.806 18 99 84
3.516 23 121 84
3.039 20 115 35
2.966 23 127 70
2.482 18 99 15
2.700 18 108 47
3.920 29 129 98
2.834 20 103 77
3.222 23 122 72
3.084 26 118 29
4.000 28 135 80
3.511 34 139 88
3.323 20 128 80
3.072 20 120 46
2.079 26 114 89
3.875 32 133 91
3.208 25 123 95
2.920 27 111 83
3.345 27 122 92
3.956 29 136 99
3.808 19 140 41
2.506 21 109 68
3.886 24 133 98
2.183 27 98 59
3.429 25 134 89
3.024 18 124 89
3.750 29 128 92
3.833 24 149 97
3.113 27 121 43
2.875 21 117 52
2.747 19 110 82
2.311 18 104 61
1.841 25 95 72
1.583 18 96 33
2.879 20 117 97
3.591 32 130 97
2.914 24 121 92
3.716 35 125 99
2.800 25 112 61
3.621 28 136 72
3.792 28 129 99
2.867 25 106 76
3.419 22 108 66
3.600 30 138 70
2.394 20 106 44
2.286 20 111 33
1.486 31 101 77
3.885 20 113 57
3.800 29 131 96
3.914 28 140 97
1.860 16 111 65
2.948 28 110 85

1.) Plot the residuals ei against the fitted values ˆyi (in R). What departures from the regression model assumptions can be studied from this plot? What are your findings? (Note:If you are not sure about the validity of any of the assumptions, perform a formal test to verify your answer.)

2.) Prepare a normal probability plot (QQ plot) of the residuals. What assumption can be tested from this plot and what do you conclude? (Note:You can also use the formal test to reinforce your conclusion).

3.) Information is given for each student on two variables not included in the model, namely,intelligence test score (ITS-x2) and high school class rank percentile (RP-x3).Plot the residuals you obtained in part (b) against x2 and x3 on separate graphs to as certain whether the model can be improved by including either of these variables. What do you conclude? (Hint:The residuals represent any variability that was not able to be explained by x1. Therefore, if you see any pattern between the residuals and any other predictor omitted from the model, there is an indication that the predictor will be useful to be added in the model.)

The average modulus of rupture (MOR) for a particular grade of pencil lead is known to be 6500 psi with a standard deviation of 250 psi.

a) Find the probability that a random sample of 16 pencil leads with have an average MOR between 6400 and 6550 psi.

1. The following table contains the demand from the last 5 months.

1. Calculate the single exponential smoothing forecast for these data using an α of 0.3 and an initial forecast (F₁) of 28. Report the forecast for Month 6 in AnswerSheet. Show your work in worksheet “Show your work for Q1.” (2 pts.)

2. Calculate the exponential smoothing with trend forecast for these data using an α of 0.25, a β of 0.60, an initial trend forecast (T₁) of 1, and an initial exponentially smoothed forecast (F₁) of 28. Report the forecast including trend (FIT) for Month 6 in AnswerSheet. Show your work in worksheet “Show your work for Q1.” (2 pts.)

3. Calculate the mean absolute deviation (MAD) for each forecast. Which forecasting method performs better in this problem (pick from the list)? Show your work in worksheet “Show your work for Q1.” (3 pts.)