For questions 1, 2, 3, 5, 6, and 7, I ONLY NEED the answer. I DO NOT need an explanation. For question 4, I need the correct answer with a brief explanation. I will give a good rating, thank you!

Question 1: There are 3 boxes below that you will have to choose the correct answer for.

Construct a 90% confidence interval for the population mean. Assume the population has a normal distribution. A sample of 15 randomly selected math majors has a grade point average of 2.86 with a standard deviation of 0.78. O (2.43, 3.29) O (2.5, 3.2) O (-0.52, 2.08) O (-0.8, 2.4)You want to estimate the mean fuel efficiency of a brand of automobiles with 99% confidence and a margin of error of no more than 2 miles per gallon. Preliminary data suggests that 12.4 miles per gallon is a reasonable estimate of the standard deviation for all cars of this make and model. How large a sample do you need? O 92 O 148 O 256 O 324Here are measurements (in millimeters) of a critical dimension on an SRS of 8 of the more than 200 auto engine crankshafts produced in one day that are known to be normally distributed: 234.12 233.91 234.21 233.96 234.07 233.98 234.09 234.15 Construct a 95% confidence interval for the mean measurements of a critical dimension at the time these crankshafts were produced.Here are measurements (in millimeters) of a critical dimension on an SRS of 8 of the more than 200 auto engine crankshafts produced in one day that are known to be normally distributed: 234.12 233.91 234.21 233.96 234.07 233.98 234.09 234.15 Interpret the 95% confidence interval calculated in the previous problem for the mean measurements of the critical dimension measured.A lab supply company sells pieces of Douglas fir 4 inches long and 1.5 inches square for force experiments in science classes. From experience, the strength of these pieces of wood follows a Normal distribution with standard deviation 2000 pounds. You want to estimate the mean load needed to pull apart these pieces of wood to within 500 pounds with 90% confidence. How large a sample is needed? Show your work (the values typed into the calculator) and your final answer.What is the critical value t* for a 99% confidence interval when n = 20?Here are measurements (in millimeters) of a critical dimension on an SRS of 8 of the more than 200 auto engine crankshafts produced in one day that are known to be normally distributed: 234.12 233.91 234.21 233.96 234.07 233.98 234.09 234.15 Check the conditions for constructing a 95% confidence interval for the mean of the critical dimension measured. 2) 3)