answer the following questions

Use a normal distribution (2 score) to construct each confidence interval. Show all work. I. A sample of 45 randomly selected students has a grade point average of 2.86. Assume the standard deviation of all students is 0.78. Construct a 90% condence interval for the population mean, u 2. In a random sample of 73 sports cars, the average annual fuel cost was $4436. Construct a 98% confidence interval for it. Assume the standard deviation for all sports cars was $523. 3. An admissions director wants to estimate the mean age of all students enrolled at a college. The estimate must be within 0.5 years of the population mean. Assume or - 1.5 . Assume the population of ages is normally distributed. Determine the minimum sample size required to construct: a) a 90% confidence interval for the population mean. b) Repeat part (a) using a 99% confidence level