Please TYPE the explanation

1.A soft-drink bottle vendor claims that its process yields bottles with a mean internal strength of 157 psi (pounds per square inch) and a standard deviation of 3 psi and is normally distributed. As part of its vendor surveillance, a bottler strikes an agreement with the vendor that permits the bottler to sample from the vendor's production to verify the vendor's claim. (10 points)

A)Suppose the bottler randomly selects 15 bottles to sample. What is the mean and standard deviation?

B)Suppose it's not normally distributed. What is the mean and standard deviation for 64 randomly selected bottles?

2.Given the following GPA for 4 students: 2, 3, 3, 4. Age of students are: 10, 11, 12, 15. There are 10,000 total students. Average GPA: Unknown, Standard Deviation of GPA: 0.02 and it's Normal.

a.Find the mean and standard deviation for GPA. (10 points)

b.Calculate a 95% confidence interval for the populations mean GPA. (5 points)

c.Use Correlation formula to find r between GPA and Age. (10 points)

d.Find Regression Line Equation. (5 points)

e.If a student's age is 13, what is the corresponding GPA? (5 points)