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Q1) For a standard normal distribution, determine the following probabilities. a) P(z>1.44) b) P(z>−0.53) c) P(−1.77≤z−0.73) d) P(−1.76≤z≤0.21) Click here to view page 1 of the standard normal probability table. LOADING… Click here to view page 2 of the standard normal probability table. LOADING… a) P(z>1.44)= (Round to four decimal places as needed.) b) P(z> −0.53)= (Round to four decimal places as needed.) c) P(−1.77≤ z ≤−0.73)= (Round to four decimal places as needed.) d) P(−1.76≤z≤0.21)= (Round to four decimal places as needed.) Q2) The average number of miles driven on a full tank of gas in a certain model car before its low-fuel light comes on is 309. Assume this mileage follows the normal distribution with a standard deviation of 41 miles. Complete parts a through d below. a. What is the probability that, before the low-fuel light comes on, the car will travel less than 340 miles on the next tank of gas? (Round to four decimal places as needed.) b. What is the probability that, before the low-fuel light comes on, the car will travel more than 256 miles on the next tank of gas? (Round to four decimal places as needed.) c. What is the probability that, before the low-fuel light comes on, the car will travel between 274 and 294 miles on the next tank of gas? (Round to four decimal places as needed.) d. What is the probability that, before the low-fuel light comes on, the car will travel exactly 284 miles on the next tank of gas? (Round to four decimal places as needed.) Q3) A credit score measures a person’s creditworthiness. Assume the average credit score for Americans is 685.Assume the scores are normally distributed with a standard deviation of 49. a) Determine the interval of credit scores that are one standard deviation around the mean. b) Determine the interval of credit scores that are two standard deviations around the mean. c) Determine the interval of credit scores that are three standard deviations around the mean. a) The interval of credit scores that are one standard deviation around the mean ranges from nothing to nothing. (Type integers or decimals. Use ascending order.) b) The interval of credit scores that are two standard deviations around the mean ranges from to . (Type integers or decimals. Use ascending order.) c) The interval of credit scores that are three standard deviations around the mean ranges from to . (Type integers or decimals. Use ascending order.) Q4) Assume the time required to pass through security at a particular airport follows the continuous uniform distribution with a minimum time of 8 minutes and maximum time of 34 minutes. Complete parts (a) through (f) below. a) Calculate the value of f(x). f(x)= (Type an integer or decimal rounded to three decimal places asneeded.) b) What are the mean and standard deviation for thisdistribution? The mean of this distribution is (Type an integer or a decimal.) The standard deviation of this distribution is (Type an integer or decimal rounded to two decimal places asneeded.) c) What is the probability that the next passenger will require less than 27 minutes to pass through security? (Type an integer or decimal rounded to three decimal places asneeded.) d) What is the probability that the next passenger will require more than 21 minutes to pass through security? (Type an integer or decimal rounded to three decimal places asneeded.) e) What is the probability that the next passenger will require between 13 and 16 minutes to pass through security? (Type an integer or decimal rounded to three decimal places asneeded.) f) What time represents the 75th percentile of thisdistribution? (Type an integer or a decimal.) Q5) For a population with a mean equal to 250 and a standard deviation equal to 35, calculate the standard error of the mean for the following sample sizes. a) 20 b) 40 c) 60 a) The standard error of the mean for a sample size of 20 (Round to two decimal places as needed.) b) The standard error of the mean for a sample size of 40 (Round to two decimal places as needed.) c) The standard error of the mean for a sample size of 60 (Round to two decimal places as needed.) Q6) For a population with a proportion equal to 0.32, calculate the standard error of the proportion for the following sample sizes. a) 35 b) 70 c) 105 a) σp= (Round to four decimal places as needed.) b) σp= (Round to four decimal places as needed.) c) σp = (Round to four decimal places as needed.) Q7) A national air traffic control system handled an average of 47,665 flights during 29 randomly selected days in a recent year. The standard deviation for this sample is 6,208 flights per day. Complete parts a through c below. a. Construct a 99% confidence interval to estimate the average number of flights per day handled by the system. The 99% confidence interval to estimate the average number of flights per day handled by the system is from a lower limit of nothing to an upper limit of nothing. (Round to the nearest whole numbers.) b. Suppose an airline company claimed that the national air traffic control system handles an average of 50,000 flights per day. Do the results from this sample validate the airlinecompany’s claim? A.Since the 99% confidence interval does not contain 50,000, it can be said with 99% confidence that the sample validates the airline company’s claim. B.Since the 99% confidence interval does not contain 50,000, it cannot be said with 99% confidence that the sample validates the airline company’s claim. C.Since the 99% confidence interval contains 50,000, it can be said with 99% confidence that the sample validates the airlinecompany’s claim. D.Since the 99% confidence interval contains 50,000, it cannot be said with 99% confidence that the sample validates the airlinecompany’s claim. c. What assumptions need to be made about this population? A.Since the sample size is not greater than or equal to 30, one needs to assume that the population distribution is not very skewed to one side. B.Since the sample size is not greater than or equal to 30, one needs to assume that the population follows the normal probability distribution. C.Since the sample size is not greater than or equal to 30, one needs to assume that the population follows the Student’s t-distribution. D.Since the sample size is not greater than or equal to 30, one needs to assume that the population distribution is skewed to one side. a. The 95% confidence interval has a lower limit of $ and an upper limit of $. (Round to the nearest cent as needed.) b. The margin of error is $ . (Round to the nearest cent as needed.) Q8) A country’s tax collection agency reported that 86% of individual tax returns were filed electronically in 2017. A random sample of 237 tax returns from 2018 was selected. From thissample, 197 were filed electronically. Complete parts a through c. a. Construct a 95% confidence interval to estimate the actual proportion of taxpayers who filed electronically in 2018. The confidence interval has a lower limit of nothing and an upper limit of nothing. (Round to three decimal places as needed.) b. What is the margin of error for this sample? The margin of error is nothing. (Round to three decimal places as needed.) c. Is there any evidence that this proportion has changed since 2017 based on this sample? This sample ▼ provides does not provide evidence that this proportion has changed since 2017, since the ▼ Q10) Determine the sample size n needed to construct a 95% confidence interval to estimate the population mean when σ=36 and the margin of error equals 6. N= Q11) Determine the sample size n needed to construct a 90% confidence interval to estimate the population proportion when p=0.39 and the margin of error equals 8%.
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