Suppose a standardized college entry exam is approximately normally distributed with =125 and =17 for each section: math, science, reading...

1.     Suppose a standardized college entry exam is approximately normally distributed with μ=125 and σ=17 for each section: math, science, reading comprehension, and logical assessment. If a student wants to be competitive for his top school of choice, what score should he/she aim to receive to be in the top 10, 5, or 1%?

1.     Suppose researchers are interested in estimating the prevalence of HIV in a population of adolescent intravenous drug users determined to equal 9.4% in the population. In order to estimate the prevalence of the disease, the researchers need to randomly sample from the population of potential participants in their study. Suppose the researchers are able to randomly sample 127 participants, and find that 29 are co-infected with the diseases of interest.

A)  Can we approximate this distribution with the normal? Why or why not?

B)  Create a Z score for this sample.

C)  What is the probability of observing at least 29 to be co-infected from sample that was collected?

1.     A population of diabetic patients at a clinic serving those awaiting a potential kidney transplant keeps records about vital patient data on reserve. Suppose the fasting glucose among the population of all potential hosts awaiting a new kidney is normally distributed with mean 137 mmol/L and standard /L. From a sample of 29 patients from the database of patients, what is the probability of the sample mean fasting glucose is between 100 and 125 mmol/L?