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)(5 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 andit'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)

4.Find P( -1.2 < Z < -0.2 ) (5 points)

5.Believe it or not, there are some people who don't think that Duke will win the NCAA tournament this year.Let's say that you want to measure the average intelligence of Duke Doubters.Problem is you could only find 28 DDs on this whole campus.The mean of your sample was 90 and the standard deviation was 60.Calculate the 90% Confidence Interval for the IQ of DDs. (10 points)

6.It is known that the mean cholesterol level for all Americans is 190.Construct the relevant hypothesis test to show that only children have an average higher cholesterol level than the national average. We test 100 only children and find out the mean is 198. You can use your own confidence level. (All Americans

Standard Deviation is 15) (10 points)

7.Newsweek performed a poll in which 567 American parents were asked the question, "Would you prefer to have your child taught by a male or female for grades K-2?"Only 12% responded that they would prefer to have their child taught by a male in grades K-2. Construct a 99% confidence interval for the poll. (10 points)

8.A nutrition store in the mall is selling "Memory Booster," which is a concoction of herbs and minerals that is intended to improve memory performance, but there is no good reason to think it couldn't possibly do the opposite. To test the effectiveness of the herbal mix, a researcher obtains a sample of 8 participants and asks each person to take the suggested dosage each day for 4 weeks. At the end of the 4-week period, each individual takes a standardized memory test. In the general population, the standardized test is known to have a mean of = 7. The scores for the 8 participants are

12, 11, 13, 15, 8, 11, 13, 15

Will those who take Memory Booster have the same memory score as that of the general population?

(Set the significance level= .05) (10 points)