Set the seed equal to 86, and simulate mi = Bin(n1, T = 20, 000 samples of size n1 = 1000 from a 0.3) and m2 = 20, 000 samples of size n2 = 1100 from a Bin(n2, 7 = = 0.7). Verify that the difference of sampling proportions follows a normal distribution.
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- Assume the random variable X is normally distributed with mean μ=50 and standard deviation σ=7. Find the 87th percentile.A population of values has a normal distribution with μ=248.4μ=248.4 and σ=23.6σ=23.6. You intend to draw a random sample of size n=32n=32.Find P18, which is the score separating the bottom 18% scores from the top 82% scores.P18 (for single values) = Find P18, which is the mean separating the bottom 18% means from the top 82% means.P18 (for sample means) = Enter your answers as numbers accurate to 1 decimal place.************NOTE************ round your answer to ONE digit after the decimal point! ***********Answers obtained using exact z-scores or z-scores rounded to 3 decimal places are accepted.A population of values has a normal distribution with μ=89.6 and σ=35.2. You intend to draw a random sample of size n=32.Find P95, which is the mean separating the bottom 95% means from the top 5% means.The mean =
- To compare the dry braking distances from 30 to 0 miles per hour for two makes of automobiles, a safety engineer conducts braking tests for 35 models of Make A and 35 models of Make B. The mean braking distance for Make A is 43 feet. Assume the population standard deviation is 4.6 feet. The mean braking distance for Make B is 46 feet. Assume the population standard deviation is 4.5 feet. At α=0.10, can the engineer support the claim that the mean braking distances are different for the two makes of automobiles? Assume the samples are random and independent, and the populations are normally distributed. The critical value(s) is/are Find the standardized test statistic z for μ1−μ2.The score on a standardized test for a certain year is modeled using the normal distribution shown below. The mean of the distribution is 56.7 points and the standard deviation is 4.8 points. In the figure, V is a number along the axis and is under the highest part of the curve. And, U and W are numbers along the axis that are each the same distance away from V. Use the empirical rule to choose the best value for the percentage of the area under the curve that is shaded, and find the values of U, V, and W. Percentage of total area shaded: (Choose one) v 68% 95% 99.7% 40 45 50 55 O 60 65 | 70 75 Test scoreCarboxyhemoglobin is formed when hemoglobin is exposed to carbon monoxide. Heavy smokers tend to have a high percentage of carboxyhemoglobin in their blood.t Let x be a random variable representing percentage of carboxyhemoglobin in the blood. For a person who is a regular heavy smoker, x has a distribution that is approximately normal. A random sample of n = 12 blood tests given to a heavy smoker gave the following results (percent carboxyhemoglobin in the blood). Note: For degrees of freedom d.f. not in the Student's t table, use the closest d.f. that is smaller. In some situations, this choice of d.f. may increase the P-value a small amount and thereby produce a slightly more "conservative" answer. 9.1 9.8 10.4 9.8 11.3 12.2 11.6 10.3 8.9 9.7 13.4 9.9 (a) Use your calculator to calculate x and s. (Round your answers to four decimal places.) X = S = (b) A long-term population mean u = 10% is considered a health risk. However, a long-term population mean above 10% is considered a…
- The height of an 8th grader is modeled using the normal distribution shown below. The mean of the distribution is 59.1 in and the standard deviation is 1.2 in. In the figure, Vis a number along the axis and is under the highest part of the curve. And, U and W are numbers along the axis that are each the same distance away from V. Use the empirical rule to choose the best value for the percentage of the area under the curve that is shaded, and find the values of U, V, and W. Percentage of total area shaded: (Choose one) V 56 58 60 62 Height (in inches)Suppose in a local Kindergarten through 12th grade (K -12) school district, 49% of the population favor a charter school for grades K through 5. A simple random sample of 144 is surveyed. a. Find the mean and the standard deviation of X of B(144, 0.49). Round off to 4 decimal places. O = b. Now approximate X of B(144, 0.49) using the normal approximation with the random variable Y and the table. Round off to 4 decimal places. Y - N( c. Find the probability that at most 81 favor a charter school using the normal approximation and the table. (Round off to z-values up to 2 decimal places.) P(X 75) - P(Y > a (Z > e. Find the probability that exactly 81 favor a charter school using the normal approximation and the table. (Round off to z-values up to 2 decimal places.) P(X = 81) - P(A food manufacturer claims that eating its new cereal as part of a daily diet lowers total blood cholesterol levels. The table shows the total blood cholesterol levels (in milligrams per deciliter of blood) of seven patients before eating the cereal and after one year of eating the cereal as part of their diets. Use technology to test the mean difference. Assume the samples are random and dependent, and the population is normally distributed. At a = 0.05, can you conclude that the new cereal lowers total blood cholesterol levels? Patient Total Blood Cholesterol (Before) Total Blood Cholesterol (After) OA. Ho Hd #0 HA Hd=0 OC. Ho Hd ≤0 HA Hd >0 Calculate the standardized test statistic t= (Round to three decimal places as needed.) Calculate the P-value P-value= (Round to four decimal places as needed) State the conclusion. 1 205 204 Ho. There C 2 225 222 Let the blood cholesterol level before eating the cereal be population 1. Let the blood cholesterol level after eating the cereal be…Suppose in a local Kindergarten through 12th grade (K -12) school district, 49% of the population favor a charter school for grades K through 5. A simple random sample of 144 is surveyed. a. Find the mean and the standard deviation of X of B(144, 0.49). Round off to 4 decimal places. O = b. Now approximate X of B(144, 0.49) using the normal approximation with the random variable Y and the table. Round off to 4 decimal places. Y - N( c. Find the probability that at most 81 favor a charter school using the normal approximation and the table. (Round off to z-values up to 2 decimal places.) P(X 75) - P(Y > a (Z > e. Find the probability that exactly 81 favor a charter school using the normal approximation and the table. (Round off to z-values up to 2 decimal places.) P(X = 81) - P(The table below shows the number of hours per day 11 patients suffered from headaches before and after 7 weeks of soft tissue therapy. At x = 0.01, is there enough evidence to conclude that soft tissue therapy helps to reduce the length of time patients suffer from headaches? Assume the samples are random and dependent, and the population is normally distributed. Complete parts (a) through (f). Patient 8 9 10 11 Q 1 Daily headache hours (before) 2.3 3.4 3.3 2.6 1.8 Daily headache hours (after) 1.8 2.7 1.8 1.6 1.9 1.9 1.2 2.5 2.2 2.0 1.1 2 3 4 5 6 7 4.1 3.2 3.5 2.4 3.7 2.6 C (a) Identify the claim and state Ho and Ha The claim is "The therapy the length of time patients suffer from headaches." Let μd be the hypothesized mean of the patients' daily headache hours before therapy minus their daily headache hours after it. State Ho and H₂. Choose the correct answer below. OA. Ho: Hd=d O C. Ho: Hd ≤0 OB. Ho. Họ sở Ha: Hd >d Ha: Hdd Ha: Hd>0 OD. Ho: Hd #d Ha:Hd=d O E. Ho: Hd zd Ha: Hd 3.169…As a part of the productivity assessment at a company, the HR manager carried out a survey and found that inclusive of overtime, the amount of time spent at work per week follows a normal distribution with µ=35 hours and σ2 = 4 hours.SEE MORE QUESTIONSRecommended textbooks for youA First Course in Probability (10th Edition)ProbabilityISBN:9780134753119Author:Sheldon RossPublisher:PEARSON
A First Course in Probability (10th Edition)ProbabilityISBN:9780134753119Author:Sheldon RossPublisher:PEARSON