Hi, i need assistance with Math homework. thank you

Assignment 1 1. Consider a family of three children. Find the following probabilities. a. P (two girls and a boy) b. P (at least one girl) c. P (children of both sexes) d. P (at least two girls) 2. A committee of four is selected from a total of 4 freshmen, 5 sophomores, and 6 juniors. Find the probabilities for the following events. a. At least three freshmen. b. All four of the same class. c. Not all four from the same class. d. Exactly three of the same class. 3. At a college, 60% of the students pass Accounting, 70% pass English, and 30% pass both of these courses. If a student is selected at random, find the following conditional probabilities. a. The student passes Accounting given that said student passed English. b. The student passes English given that said student passed Accounting. 4. John's probability of passing statistics is 40%, and Linda's probability of passing the same course is 70%. If the two events are independent, find the following probabilities. a. P(both of them will pass statistics) b. P(at least one of them will pass statistics) 5. A $1 lottery ticket offers a grand prize of $10,000; 10 runner-up prizes each paying $1000; 100 third-place prizes each paying $100; and 1,000 fourth-place prizes each paying $10. Find the expected value of entering this contest if 1 million tickets are sold. Assignment 2 Statistics For this assignment, you will implement a project involving statistical procedures. The topic may be something that is related to your work, a hobby, or something you found interesting. If you choose, you may use the example described below. This report must include *name of report and your name *purpose of report *Data (provide the raw data used, and cite the source)the sample size must be at least 10 *median, sample mean, range, sample variance, and sample standard deviation (show work) *frequency distribution *histogram *percentage of data within one standard deviation of the mean, percentage of data within two standard deviations of the mean, percentage of data within three standard deviations of the mean (include explanation and interpretation --- do your percentages imply that the histogram is approximately bell-shaped?) Conclusion (several paragraphs interpreting your statistics and graphs; relate to the purpose of the project) If you choose, you may use the following example for your data. *Purpose: Compare the amount of sugar in a standard serving size of different brands of cereal. (You may instead choose to compare the amount of fat, protein, salt, or any other category in cereal or some other food.) *Procedure: Go to the grocery store (or your pantry) and pick at least 10 different brands of cereal. (Instead of choosing a random sample, you might purposely pick from both the "healthy" cereal types and the "sugary" ones.) From the cereal box, record the suggested serving size and the amount of sugar per serving. The raw data is the serving size and amount of sugar per serving for each of the 10 boxes of cereal. Before calculating the statistics on the amount of sugar in each cereal, be sure you are comparing the same serving size. If you use a serving size of 50 grams, you must calculate how much sugar is in 50 grams of each cereal. For example, if the box states that there are 9 grams of sugar in 43 grams of cereal, there would be 50 times 9 divided by 43, or 10.5 grams in 50 grams of cereal. The result of this simple calculation (for each of 10 boxes) is the data you will use in the project statistics and charts. Can you please calculate the mean, median, and mode of this data? The number between interval 61 70 are 61and 67, so frequency is 2. There is no number between intervals 71 80 , so frequency is 0. The number between interval 81 90 are 81, 83, 87, 88, 89 and 90, so frequency is 6. The number between interval 91 100 are 98 and 100, so frequency is 2. Complete the frequency table as shown below: Interval 61 70 71 80 81 90 91 100 Frequency 2 0 6 2 Can you please calculate the mean, median, and mode of this data? The number between interval 61 70 are 61and 67, so frequency is 2. There is no number between intervals 71 80 , so frequency is 0. The number between interval 81 90 are 81, 83, 87, 88, 89 and 90, so frequency is 6. The number between interval 91 100 are 98 and 100, so frequency is 2. Complete the frequency table as shown below: Interval 61 70 71 80 81 90 91 100 Frequency 2 0 6 2 1. The test scores for 10 students in Ms. Sampson'shomeroom were 61, 67, 81, 83, 87, 88, 89, 90,98, and 100. Complete the frequency table. Interval 61 - 70 71 - 80 81 - 90 91 - 100 Frequency 1 Assignment 2: Salt in Soups - a comparison of some popular types and brands: BY: Type your name here The purpose of these statistical analyses is to compare the amount of salt in different soup brands. For this comparison study, we have selected 12 soups from a local grocery store and recorded the amount of salt (sodium) in each. The serving size is 1 cup (8 oz) for all entries in this table The raw data are listed in the table below. Brand Healthy Choice Minestrone Campbell's Condensed Tomato Soup (Healthy Request) Campbell's Condensed Tomato Soup Campbell's Condensed Cream of Mushroom Campbell's Select Harvest 100% Natural Harvest Tomato with Basil Progresso Traditional 99% Fat-free Chicken Noodle Progresso Rich and Hearty Steak and Vegetables Progresso Vegetable Classics Garden Vegetable Campbell's Condensed Cream of Broccoli Progresso Traditional 99% Fat-free New England Clam Chowder Campbell's Chunky Beef with Country Vegetables Campbell's condensed Manhattan Clam Chowder Sodium /cup 360 Cups/can 2 Sodium/can 360 2 720 410 2.5 410 2.5 1025 480 3.5 480 2.5 1200 650 2 650 2 1300 650 2 650 2 1300 670 2 670 2 1340 690 2 690 2 1380 690 2 690 2 1380 750 2.5 750 2.5 1875 810 2 810 2 1620 870 2.5 870 2.5 2175 880 2.5 880 2.5 2200 We will compute statistics using the sodium per cup values. The maximum value is 880 and minimum value is 360, so range is Range Maximum Minimum 880 360 520 Thus, the range is 520 . Calculate the mean as 360 410 480 650 650 670 690 690 750 810 870 880 12 7910 12 659.2 Mean Thus, the mean is 659.2 . Since the sample size is even (12), so median is n n 1th term th term 2 2 Median 2 12 12 th term 1th term 2 2 2 6th term 7th term 2 670 690 2 680 Thus, the median is 680 . For each number subtract the mean and square the result: n 12 360 659.2 89520.64 2 410 659.2 62100.64 2 480 659.2 32112.64 2 650 659.2 84.64 2 650 659.2 84.64 2 670 659.2 116.64 690 659.2 948.64 2 690 659.2 948.64 2 750 659.2 8244.64 2 810 659.2 22740.64 2 870 659.2 44436.64 2 880 659.2 48752.64 2 2 Calculate standard deviation as 89520.64 62100.64 32112.64 84.64 84.64 116.64 948.64 948.64 8244.64 22740.64 44436.64 48752.64 Standrad deviation 12 310091.68 12 167.9 Thus, the standard deviation is 167.9 . The normal distribution curve is shown below: Three standard deviation Two standard deviation One standard deviation Out of 12 data, 8 is between one standard deviation of mean 491.3 and 659.2, so 8 100 12 67% % within 1 Out of 12 data, 12 is between two standard deviation of mean 323.4 and 995, so 12 100 12 100% % within 2 Out of 12 data, 12 is between three standard deviation of mean 115.5 and 1162.9, so 12 100 12 100% % within 3 The frequency distribution table is shown below: Interval 0 200 200 400 400 600 600 800 800 1000 1000-1200 Frequency 0 1 2 6 3 0 The histogram is shown below: From the above figure we see the data are roughly bell-shaped, but are slightly skewed to the low-sodium side. Conclusion: The purpose of these statistical analyses is to compare the amount of salt in different soup brands. The range compares the minimum amount of Sodium /cup to the maximum amount of Sodium /cup. It doesn't tell much about the shape of distribution and how it varies from the mean. The standard deviation tells what is happening between amount of Sodium /cup to the maximum amount of Sodium /cup. It tells how much the data vary around mean. Since the mean 659.2 is less than the median 680, the distribution has a negative skew. This means the entries lower than median are farther away from the median than the entries higher than the median. Reference: http://www.hellawella.com/infographic-125-popular-soups-ranked-by-sodiumcontent/9067 Assignment 2: Salt in Soups - a comparison of some popular types and brands: BY: Type your name here The purpose of these statistical analyses is to compare the amount of salt in different soup brands. For this comparison study, we have selected 12 soups from a local grocery store and recorded the amount of salt (sodium) in each. The serving size is 1 cup (8 oz) for all entries in this table The raw data are listed in the table below. Brand Healthy Choice Minestrone Campbell's Condensed Tomato Soup (Healthy Request) Campbell's Condensed Tomato Soup Campbell's Condensed Cream of Mushroom Campbell's Select Harvest 100% Natural Harvest Tomato with Basil Progresso Traditional 99% Fat-free Chicken Noodle Progresso Rich and Hearty Steak and Vegetables Progresso Vegetable Classics Garden Vegetable Campbell's Condensed Cream of Broccoli Progresso Traditional 99% Fat-free New England Clam Chowder Campbell's Chunky Beef with Country Vegetables Campbell's condensed Manhattan Clam Chowder Sodium /cup 360 Cups/can 2 Sodium/can 360 2 720 410 2.5 410 2.5 1025 480 3.5 480 2.5 1200 650 2 650 2 1300 650 2 650 2 1300 670 2 670 2 1340 690 2 690 2 1380 690 2 690 2 1380 750 2.5 750 2.5 1875 810 2 810 2 1620 870 2.5 870 2.5 2175 880 2.5 880 2.5 2200 We will compute statistics using the sodium per cup values. The maximum value is 880 and minimum value is 360, so range is Range Maximum Minimum 880 360 520 Thus, the range is 520 . Calculate the mean as 360 410 480 650 650 670 690 690 750 810 870 880 12 7910 12 659.2 Mean Thus, the mean is 659.2 . Since the sample size is even (12), so median is n n th term 1th term 2 2 Median 2 12 12 th term 1th term 2 2 2 6th term 7th term 2 670 690 2 680 Thus, the median is 680 . n 12 For each number subtract the mean and square the result: 360 659.2 89520.64 2 410 659.2 62100.64 2 480 659.2 32112.64 2 650 659.2 84.64 2 650 659.2 84.64 2 670 659.2 116.64 690 659.2 948.64 2 690 659.2 948.64 2 750 659.2 8244.64 2 810 659.2 22740.64 2 870 659.2 44436.64 2 880 659.2 48752.64 2 2 Calculate standard deviation as 89520.64 62100.64 32112.64 84.64 84.64 116.64 948.64 948.64 8244.64 22740.64 44436.64 48752.64 Standrad deviation 12 310091.68 12 167.9 Thus, the standard deviation is 167.9 . The normal distribution curve is shown below: Three standard deviation Two standard deviation One standard deviation Out of 12 data, 8 is between one standard deviation of mean 491.3 and 659.2, so 8 100 12 67% % within 1 Out of 12 data, 12 is between two standard deviation of mean 323.4 and 995, so 12 100 12 100% % within 2 Out of 12 data, 12 is between three standard deviation of mean 115.5 and 1162.9, so 12 100 12 100% % within 3 The frequency distribution table is shown below: Interval 0 200 200 400 400 600 600 800 800 1000 1000-1200 Frequency 0 1 2 6 3 0 The histogram is shown below: From the above figure we see the data are roughly bell-shaped, but are slightly skewed to the low-sodium side. Conclusion: The purpose of these statistical analyses is to compare the amount of salt in different soup brands. The range compares the minimum amount of Sodium /cup to the maximum amount of Sodium /cup. It doesn't tell much about the shape of distribution and how it varies from the mean. The standard deviation tells what is happening between amount of Sodium /cup to the maximum amount of Sodium /cup. It tells how much the data vary around mean. Since the mean 659.2 is less than the median 680, the distribution has a negative skew. This means the entries lower than median are farther away from the median than the entries higher than the median. Reference: http://www.hellawella.com/infographic-125-popular-soups-ranked-by-sodiumcontent/9067