Could you please solve this using R?

The information on people's health risk factors DOES NOT APPLY to the following questions.

17- A research team wants to examine the relationship between health status and income among the adult patients of a hospital.

They randomly sampled 2000 adult patients, and surveyed their income. The first, second, and third quartiles are $35700, $53000, and $82400. The researchers also classified these patient's health status into poor, fair, and good.

We know that 265 of the patients in the first income quartile have poor health; 185 in the second income quartile have poor health; 120 in the third quartile have poor health; and 30 in the fourth quartile have poor health.

What is the probability that a patient who has fair or better health status makes more than the median income? Show your work.

18- A student's grade in a course is determined by their scores on assignments, exams, and the number of missed class days. Suppose the final grade is calculated as the total of 40% of the assignment score and 60% of the exam score, and reduced by 10% of the number of missed class days. For example, if a student earned 90 in assignments, 80 in exams, and missed 1 day of class, his/her final score is 0.4*90 + 0.6*80 - 0.1*1 = 83.9.

From historical data we know that the assignment score has mean of 85 and standard deviation of 10; and the exam score has mean of 80 and standard deviation of 15. We also know that the mean and standard deviation of missed class days are 2 and 0.5.

What are the mean and standard deviation of the final score, assuming the assignment score, exam score, and number of missed class days are independent? Show your work.

19- A researcher wants to examine babies' weights at birth of a minority population. She collects a simple random sample of 50 birth weights from this minority population. She calculated that the average weight in this sample is 3145 grams, and the standard deviation is 203 grams.

Calculate a 95% confidence interval of the mean birth weight of this minority population. Show your work.

20 - In the same study from the previous question, the researcher suspects that these babies weigh less than the US population mean of 3250 grams due to potential malnutrition.

Carry out a hypothesis test (at significant level 0.05) to check her suspicion. Show your work, including the hypotheses, the calculation, and your conclusion in the context of this problem.