A random sample of 90 observations produced a mean of x = 34.6 from a population with a normal distribution and a standard deviation o = 4.77. (a) Find a 95% confidence interval for µ <μ< (b) Find a 99% confidence interval for u <μ< (c) Find a 90% confidence interval for μ <μ <
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- For a population with mean of μ X = 30 and standard deviation of σ X = 4 , the z-score corresponding to X = 28 is:A population of values has a distribution with μ=52.4μ=52.4 and σ=72.7σ=72.7. You intend to draw a random sample of size n=205n=205.According to the Central Limit Theorem:(a) What is the mean of the distribution of sample means?μ¯x=μx¯= (b) What is the standard deviation of the distribution of sample means?(Report answer accurate to 2 decimal places.)σ¯x=σx¯=A random sample of 49 measurements from one population had a sample mean of 16, with sample standard deviation 5. An independent random sample of 64 measurements from a second population had a sample mean of 19, with sample standard deviation 6. Test the claim that the population means are different. Use level of significance 0.01. (B) Compute x1 − x2. x1 − x2 = (C) Compute the corresponding sample distribution value. (Test the difference μ1 − μ2. Round your answer to three decimal places.)
- A company claims that the mean monthly residential electricity consumption in a certain region is more than 860 kiloWatt-hours (kWh). You want to test this claim. You find that a random sample of 69 residential customers has a mean monthly consumption of 880 kWh. Assume the population standard deviation is 126 kWh. At α=0.01, can you support the claim? Complete parts (a) through (e). Also find the critical values.A population of values has a normal distribution with μ=11 and σ=41.1. If a random sample of size n=15 is selected, Find the probability that a single randomly selected value is greater than 13.1. P(X > 13.1) = Find the probability that a sample of size n=15 is randomly selected with a mean greater than 13.1. P(M > 13.1) =A population of values has a normal distribution with μ=116.3μ=116.3 and σ=27.5σ=27.5. You intend to draw a random sample of size n=249n=249.Find the probability that a single randomly selected value is greater than 117.3.P(X > 117.3) = Find the probability that a sample of size n=249n=249 is randomly selected with a mean greater than 117.3.P(¯xx¯ > 117.3) = Enter your answers as numbers accurate to 4 decimal places. Answers obtained using exact z-scores or z-scores rounded to 3 decimal places are accepted.
- state whether or not this resulting observed interval ended up capturing the true population proportion p of 0.45.A company claims that the mean monthly residential electricity consumption in a certain region is more than 860 kilo Watt-hours (kWh). You want to test this claim. You find that a random sample of 69 residential customers has a mean monthly consumption of 890 kWh. Assume the population standard deviation is 123 kWh. At α=0.05, can you support the claim? Complete parts (a) through (e). (b) Find the critical value(s) and identify the rejection region(s). Select the correct choice below and fill in the answer box within your choice. Use technology. (Round to two decimal places as needed.) A. The critical values are ±enter your response here. B. The critical value is enter your response here.A population of values has a distribution with μ=5.6μ=5.6 and σ=28.5σ=28.5. You intend to draw a random sample of size n=22n=22. According to the Central Limit Theorem: (a) What is the mean of the distribution of sample means? μ¯x=μx¯= (b) What is the standard deviation of the distribution of sample means? (Report answer accurate to 2 decimal places.) σ¯x=σx¯= (c) In a random sample of n=22, what is the probability that its sample mean is more than 4.6? Round to three decimal places. (d) In a random sample of n=22, what is the probability that its sample mean is less than 17.9? Give your answer to three decimal places. Submit
- Vehicle speeds at a certain highway location are believed to have approximately a normal distribution with mean µ = 50 mph and standard deviation σ = 5 mph. The speeds for a randomly selected sample of n = 25 vehicles will be recorded. (a) Give numerical values for the mean and standard deviation of the sampling distribution of possible sample means for randomly selected samples of n = 25 from the population of vehicle speeds. Mean = s.d.(x) = (b) Use the Empirical Rule to find values that fill in the blanks in the following sentence. For a random sample of n = 25 vehicles, there is about a 95% chance that the mean vehicle speed in the sample will be between and mph. (c) Sample speeds for a random sample of 25 vehicles are measured at this location, and the sample mean is 59 mph. Given the answer to part (b), explain whether this result is consistent with the belief that the mean speed at this location is μ = 50 mph. A sample mean of 59 mph (when n = 25) --Select--- be consistent with…A population of values has a normal distribution with μ=129.7μ=129.7 and σ=7.7σ=7.7. You intend to draw a random sample of size n=10n=10.Find the probability that a single randomly selected value is less than 130.9. P(X < 130.9) = Find the probability that a sample of size n=10n=10 is randomly selected with a mean less than 130.9. P(M < 130.9) = Enter your answers as numbers accurate to 4 decimal places. Answers obtained using exact z-scores or z-scores rounded to 3 decimal places are accepted.A population of values has a distribution with μ=213.4μ=213.4 and σ=5.8σ=5.8. You intend to draw a random sample of size n=38n=38.According to the Central Limit Theorem: What is the mean of the distribution of sample means?μ¯x=μx¯= What is the standard deviation of the distribution of sample means?(Report answer accurate to 2 decimal places.)σ¯x=σx¯=