Hi, I'm really struggling on this homework, im not sure about my answer I want to make sure my answer are correct. I also don't know how to start problem 2 going to Venn diagram ,but does not seems appropriate. I would also appreciate an explanation. Thank you!

1. A state has three counties, each with a population of approximately one million (assume equal populations). A researcher who wishes to estimate mean income earned for state residents randomly selects 100 individuals from each county and records their earned income from the past year. The sample means from each county are $40,000, $60,000 and $98,000.

a. What is the variable of interest? MEAN INCOME EARNED FOR STATE RESIDENTS

b. What is the variable and measurement scale? QUANTITATIVE VARIABLE AND INTERVAL SCALE

c. What sampling protocol is being used? SIMPLE RANDOM SAMPLE

d. What is the sample mean (of the entire sample)? 198,000

2. A female who has virus A has a one-year survival rate of 20%. A male who has virus A has a one-year survival rate of 40%. If we randomly select 5 females and 5 males (assume independence within and between groups),

a. Determine the probability at least 2 females survive more than one year.

b. Determine the probability at least 2 males survive more than one year.

c. Determine the probability at least exactly 2 people survive (regardless of sex) more than one year.

d. Determine the mean number of people who survive more than one year.

3. A new test for Virus A has 98% sensitivity and 97% specificity. If 4% of the population has virus A,

a. Determine the positive predictive value of the test ANSWER =0.576

b. Determine the negative predictive value of the test ANSWER =0.999

c. *(bonus) If tests are independent, determine the probability you have the virus if you test positive in two of two tests.

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