Random variable X has mean μX = 24 and standard deviation σX = 6. Random variable Y has mean μY = 14 and standard deviation σY = 4. A new random variable Z was formed, where Z = X + Y. What can we conclude about X, Y, and Z with certainty? That is, which one is true?
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Random variable X has
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- 8. An HP laser printer is advertised to print text documents at a speed of 18 ppm (pages per minute). The manufacturer tells you that the printing speed is actually a Normal random variable with a mean of 17.57 ppm and a standard deviation of 3 ppm. A Brother brand printer can print an average of 17.21 ppm and a standard deviation of 4 pages and its printer speed is also normally distributed. You select 10 of each printer at random. What is the probability that mean Brother print speed is at least 2 pages faster than the mean HP print speed?What is the probability that 46 cars chosen at random will have a mean load weight x of less than 85.5 tons of coal if the mean is 86 and standard deviation 1.4You are interested in studying the average gestational length of pregnancies among African American women in the United States to see if it is different from the rest of the US population. The population mean for gestational length is 39 weeks with a standard deviation of 2 weeks. You take a simple random sample of 22 African American women that gave birth in the last year and find that their mean gestational length is is 38.5 weeks. If you decide to conduct a two-sided test with α = .05. What is the power of this test?
- Help with these three questions, all three questions go together.The mean height of a certain kind of plant is 170 centimeters. Suppose we want to carry out a hypothesis test to see if the mean height when these plants are treated with a certain chemical differs from 170. State the null hypothesis H0 and the alternative hypothesis H1 that we would use for this test.A company manager plans to purchase a machine. The company requires a high quality machine. The manager is currently considering two companies that supply this machine. The machine from company A can produce approximately1050 units in average per day, but the standard deviation of this machine is about 250 units per day; while the machine from company B can produce approximately 900 units in average per day, but the standard deviation of this machine is about 100 units per day. Both of these two companies guarantee at least 10 years life. In addition, both prices are similar although machine A is a little bit higher. Price is not the main concern for the manager because both prices are under their budget. However, the manager cannot decide which machine should be purchased, because he is not sure what test he needs to conduct. Can you recommend the manager what test the manager should conduct? Should the manager conduct the test about the difference between two population means or the…
- Group A has 12 people and it is a random sample and they have an average heart rate of 100 and their standard deviation is 5. Group B has 18 people and their average heart rate is 90 and they have a standard deviation of 6. do these sample statistics provide sufficient evidence at a=0.01 to claim that the average heart rate for the population of group A is statistically greater than the heart rate of the population of group B?One tail Scenario Your company makes lamps and is able to manufacture 100 per week with a standard deviation of 10. The new CEO says that this is too low and wants to increase production. So, he purchases a new production machine. After 49 days, the average amount of lamps produced (with the added machine) is now 115 per week. He wants to test if the new machine has made a statistically significant difference. Conduct an eight-step hypothesis test to determine if the new machine has made a statistically significant difference.A statistical test is designed to show that the mean u is different from 100, state the null hypothesis (Ho) and the alternative hypothesis (Ha) to be tested.
- A particular fruit's weights are normally distributed, with a mean of 635 grams and a standard deviation of 27 grams. If you pick one fruit at random, what is the probability that it will weigh between 589 grams and 658 grams? Express your answer in 4 decimal places.Be quick please3) Over repeated samples, the sample mean is considered a random variable. Is this statement TRUE or FALSE? Select one: True False 4) If the sample correlation coefficient has a value different from zero, this automatically means that the correlation in the population is also different from zero. Is this statement correct? Explain.