Find the critical value z , needed to construct a confidence interval with level 80%. Round the answer to two decimal places. The critical value for the 80% confidence level isA sample of size n = 58 is drawn from a population whose standard deviation is o = 18. Part 1 of 2 (a) Find the margin of error for a 99% confidence interval for u. Round the answer to at least three decimal places. The margin of error for a 99% confidence interval for u is Part 2 of 2 (b) If the confidence level were 90%, would the margin of error be larger or smaller? (Choose one) , because the confidence level is (Choose one)A population has standard deviation 0' = 17.6. {a} How large a sample must be drawn so mat'a 98% condence interval for p. will have a margin of error equal to 3.2? Round Hie critical value to no less than three decimal places. Round the sample size up to the'nearest integer. A sample size of is needed to be drawn in order to obtain a 98% condence interval With a margin of error equal to 3.2. (b} If the required confidence level were 99.5%, would the necessary sample siie be larger or smaller? , because the condence level is [Choose one} I" . Itchoose one) 7 SAT scores: A college admissions officer takes a simple random sample of 100 entering freshmen and computes their mean mathematics SAT score to be 446. Assume the population standard deviation is o = 115. Part: 0 / 4 Part 1 of 4 (a) Construct a 99% confidence interval for the mean mathematics SAT score for the entering freshman class. Round the answer to the nearest whole number. A 99% confidence interval for the mean mathematics SAT score isWatch your cholesterol: A sample of 305 patients between the ages of 38 and 82 were given a combination of drugs ezetimibe and simvastatin. They achieved a mean reduction in total cholesterol of 0.80 millimole per liter. Assume the population standard deviation is o = 0.20. Part: 0 / 3 Part 1 of 3 (a) Construct an 80% confidence interval for the mean reduction in total cholesterol in patients who take this combination of drugs. Round the answer to at least two decimal places. An 80% confidence interval for the mean reduction in cholesterol isHow smart is your phone? A random sample of 8 Samsung Galaxy smartphones being sold over the Internet in 2013 had the following prices, in dollars: 199 169 385 329 269 149 135 249 Send data to Excel Assume the population standard deviation is o = 81. Perform the following. Part: 0 / 3 Part 1 of 3 (a) Explain why it is necessary to check whether the population is approximately normal before constructing a confidence interval. It is necessary to check whether the population is approximately normal because (Choose one)Lifetime of electronics: In a simple random sample of 100 electronic components produced by a certain method, the mean lifetime was 125 hours. Assume that component lifetimes are normally distributed with population standard deviation o = 20 hours. Round the critical value to no less than three decimal places. Part: 0 / 2 Part 1 of 2 (a) Construct an 80% confidence interval for the mean battery life. Round the answer to the nearest whole number. An 80% confidence interval for the mean battery life isEfcient manufacturing: Efciency experts study the processes .used to manafacture items In order to make them as efcient as possible. one of the steps used to manufacture a metal clamp involves the drilling of three holes. In a sample of 95 clamps, the mean time to complete this step was 45.? seconds. Assume that the population standard deviation is o = 10 seconds. Round the critical value to rio _less.than three decimal places. (a) Construct an 30% condence interval for the mean time-needed to complete this step. Round the answer to at least one decimal place. An 80% confidence-interval for the mean is {p &lt