Solve the following questions   

1. A bag has 4 types of coins as given below:

    • Two $1

    • Three $5

    • One $10

    • Three $20

a. Construct a probability distribution table for the data.

b. Calculate the variance.

2.  One Market Research company determined that 13% of college students work part-time during the academic year. For a random sample of 5 students, what is the probability that at least 3 students work part-time?

3. Find 

a) P(z < 2.37)
b) P(z > -1.18)
c) P(-1.18 < z < 2.37)

4. Cream cheese is sold in cans that have a net weight of 8 ounces.  The weights are normally distributed with a mean of 8.025 ounces and a standard deviation of 0.125 ounces.  You take a sample of 36 cans. Compute the probability that the sample would have a mean 7.995 ounces or more.

5. Suppose you survey that a random sample of 150 people from one hospital has been given cholesterol tests, and 60 of these people had levels over the "safe" count of 200.  Construct a 95% confidence interval for the population proportion of people in test with cholesterol levels over 200.

6. This is observation from previous years about the impact of students working while they are enrolled in classes, due to students too much work, they are spending less time on their classes. First, the observer need to find out, on average, how many hours a week students are working. They know from previous studies that the standard deviation of this variable is about 5 hours. A survey of 200 students provides a sample mean of 7.10 hours worked. What is a 95% confidence interval based on this sample?