Question 1 (2 points)

1. (1 pt) For a standard normal distribution Z ~ N(0,1) what is the value for the quantile q that leaves 10% probability in the left and right tails of the distribution combined, that is, Pr(-q < Z < q) = 0.90?

2. (1 pt) What is the quantile notation of the quantile q from question a. above?

Question 2 (6 points)

1. (2 pts) The distribution of hemoglobin among newborns is approximately normal, with a mean of 18 g/dL and SD of 3 g/dL. Values within the middle 90% of the distribution are considered in the healthy range. What is the healthy range of hemoglobin for this population?

2. (2 pts) A neonatologist treats newborns if their hemoglobin level is outside the middle 95% of the distribution. What are the upper and lower levels of hemoglobin that will trigger treatment?

3. (2 pts) A newborn has hemoglobin of 22 g/dL. What percentile does this level correspond to in this population? (For example, 70% percentile would mean that 70% of the neonates have lower hemoglobin levels, and 30% have higher levels than this newborn.)

Question 3 (6 points) Assume that serum potassium levels in a healthy population are normally distributed, with a mean of 4.5 mEq/L and a standard deviation of 0.6 mEq/L.

1. (2 pts) What proportion of the population has serum potassium levels between 4.2 and 4.8 mEq/L?

2. (2 pts) If repeated samples of size n=36 were selected, what proportion of these samples would have means between 4.2 and 4.8 mEq/L? Hint: use Central Limit Theorem

3. (2 pts) One sample of size n=36 had sample mean =4.4. What is the 95% confidence interval for the mean serum potassium in the population? (Assume the standard deviation in the population is known to be 0.6 mEq/L.)

4. Extra credit (2 points) A researcher would like to do a study that derives a confidence interval for the mean serum potassium (similar to that in question 1.c). However, the researcher wants a margin of error of 0.08 mEq/L. How many participants are needed?

Question 4 (6 points) A study is trying to determine the mean fasting (total) cholesterol of teenage boys in the US. The study collects data on 49 boys and finds a mean cholesterol of 195 mg/dL and a standard deviation of 50 mg/dL.

1. (2 pts) Which of the following is correct? Explain why.

   1. = 195 mg/dL ii. = 195 mg/dL

2. (2 pts) Which of the following is correct? Explain why.

   1. s = 50 mg/dL ii. = 50 mg.dL

3. (2 pts) Compute a 95% confidence interval for the mean fasting cholesterol in the population, based on the study results. Note: use the sample standard deviation as an estimate of the population standard deviation.