Please help me with these. I need to shows all works . Thank you in advance.
1.Each person has a 75% probability of going to the Ches Tahoe restaurant. a. You randomly select 8 people. What is the probability that 5 people will not go to the restaurant? (Calculation is necessary to get FULL credits) (10 points) b. You randomly select 50 people. Use normal approximation to find the probability that at least 35 people will go to the restaurant. Solve it by Binomial (5 points, Calculation is NOT necessary) 2. 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? 3. 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. (10 points) C. Use Correlation formula to find r between GPA and Age. (10 points) d. Find Regression Line Equation. (10 points) e. If a student's age is 13, what is the corresponding GPA? (5 points). Each person has a 75% probability of going to the Ches Tahoe restaurant. a. You randomly select 8 people. What is the probability that 5 people will not go to the restaurant? (Calculation is necessary to get FULL credits) (10 points) b. You randomly select 50 people. Use normal approximation to find the probability that at least 35 people will go to the restaurant. Solve it by Binomial (5 points, Calculation is NOT necessary) 2. 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? 3. 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. (10 points) c. Use Correlation formula to find r between GPA and Age. (10 points) d. Find Regression Line Equation. (10 points) e. If a student's age is 13, what is the corresponding GPA? (5 points)
