EXERCISE NO. 4: NORMAL RANDOM VARIABLES COMPLETING THE TABLE: Use empirical rule to complete the following table. Write on the respective column the range or interval of the scores based on the given parameters. Mean Standard 68% Pr(p-o
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- A large chemistry course took their final exam. The mean was 75 with a standard deviation of 8. What are the exam scores that separate the top and bottom 5 percent of the class (extreme 10%) 2. What are the exams scores that separate the middle 10% of the class (5% on each side of the mean)? Use table below and draw normal distributionThe absolute tolerance is +-0.01A company that manufactures batteries used in electric cars is reporting that their newest model of battery has a mean lifetime, µ, of 18 years. To test the company's claim, a competitor has selected 56 of these batteries at random. The mean lifetime of the sample is 18.9 years. Suppose the population standard deviation of these lifetimes is known to be 4.8 years. Is there enough evidence to reject the claim that the mean lifetime of the newest model is 18 years? Perform a hypothesis test, using the 0.05 level of significance. (a) State the null hypothesis H, and the alternative hypothesis H,. Ho: 0 OTwo independent samples from normal distributions are being compared. The sample data are summarized in the table. Population Populationmean Samplesize Samplemean Sample standarddeviation Standard errorestimate 1 ?1 ?1=16 x¯1=15.3 s1=2.010 SE1=0.503 2 ?2 ?2=14 x¯2=13.8 s2=2.330 SE2=0.623 The estimated standard error of the difference of the two sample means is SE=0.800. Compute the value of the two-sample ?t‑statistic used to test the null hypothesis ?0:?1=?2H0:μ1=μ2. Please give your answer precise to three decimal places.Fuel consumption of taxis at an unnamed taxi rank follows a normal distribution with an average of 15 liters / 100km and the standard deviation of 5 liters / 100km. Nonni randomly selects 12 taxis from the station and examines the average consumption of these 12 cars. What is the standard error of average consumption? 1. 5 12 2. V5 3. 5 12 V12Test a claim that the mean amount of lead in the air in U.S. cities is less than 0.036 microgram per cubic meter. It was found that the mean amount of lead in the air for the random sample o 57 U.S. cities is 0.039 microgram per cubic meter and the standard deviation is 0.069 microgram per cubic meter. At α=0.10, can the claim be supported? Complete parts (a) through (e) below. Assume the population is normally distributed.Medical Operations The director of a medical hospital feels that her surgeons perform fewer operations per year than the national average of 211. She selected a random sample of 15 surgeons and found that the mean number of operations they performed was 209.3. The standard deviation of the sample was 3.8. Is there enough evidence to support the director's feelings at =α0.01? Assume that the population is approximately normally distributed. Use the critical value method and tables.Test the claim that the mean GPA of night students is significantly different than 2.8 at the 0.1 significance level. Based on a sample of 70 people, the sample mean GPA was 2.81 with a standard deviation of 0.03 The positive critical value is: (to 2 decimals)A random sample of n1 = 49 measurements from a population with population standard deviation ?1 = 3 had a sample mean of x1 = 10. An independent random sample of n2 = 64 measurements from a second population with population standard deviation ?2 = 4 had a sample mean of x2 = 12. Test the claim that the population means are different. Use level of significance 0.01. (a) Check Requirements: What distribution does the sample test statistic follow? Explain. The Student's t. We assume that both population distributions are approximately normal with known standard deviations.The standard normal. We assume that both population distributions are approximately normal with known standard deviations. The Student's t. We assume that both population distributions are approximately normal with unknown standard deviations.The standard normal. We assume that both population distributions are approximately normal with unknown standard deviations. (b) State the hypotheses. H0: ?1 = ?2;…Photon is a training device that is designed to improve a user's reaction time. Similar devices have been criticized for being too easy to master, but the makers of Photon say that their device is built to give most users room to improve. The makers say that even among professional athletes, the proportion, p, who can score the top ranking of "light speed" is less than 18%. A random sample of 115 professional athletes is chosen, and 15 score a ranking of "light speed" while using the device. Complete the parts below to perform a hypothesis test to see if there is enough evidence, at the 0.05 level of significance, to support the claim that the proportion of all professional athletes who can score a ranking of "light speed" is less than 18%. (a) State the null hypothesis H, and the alternative hypothesis H, that you would use for the test. Oロ H: ロ=ロ ローロ (b) For your hypothesis test, you will use a Z-test. Find the values of np and n (1-p) to confirm that a Z-test can be used. (One…Medical Operations The director of a medical hospital feels that her surgeons perform more operations per year than the national average of 211. She selected a random sample of 15 surgeons and found that the mean number of operations they performed was 213.2. The standard deviation of the sample was 3.8. Is there enough evidence to support the director's feelings at =α0.05? Assume that the population is approximately normally distributed. Use the critical value method and tables. State the hypotheses and identify the claim. H0: Is a claim or not a claim H1: is a claim or is not a claim Find the critical value: Compute the test value: Make the decision Summarize the results. There is or is not enough evidence to support the claim.Hypodermic needles are produced in a manufacturing process. The quality feature to be monitored is the outside diameter (in mm) for which the target value=0.8 is specified. We assume that the outside diameter is due to production-related variations Mμ, 02)- distributed. In the course of monitoring the process, a test random sample is taken from the ongoing production N=10 needles removed. The sample mean (arithmetic mean) is 0.827, which is the sample standard deviation (empirical standard deviation).s(x) = 0.05 a) Are the data compatible with the hypothesis that the target value0=0.8 is maintained on average in the overall production? Test this HO: με μό 1:06μ to the significance levela- 5%. The quantiles required for the test are included Rto determine. In your solution, indicate the command used for this. against b) How small or how large should the sample mean of a sample with a size of N=10 with the same sample standard deviation, so that the null hypothesis in part a) is…SEE MORE QUESTIONS