Question 1 (2 points) (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 (1 pt) What is the quantile notation of the quantile q from question a above Question 2 (6 points) (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 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 (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 (2 pts) What proportion of the population has serum potassium levels between 4 2 and 4 8 mEq L (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 (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 ) 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 (2 pts) Which of the following is correct Explain why 195 mg dL ii 195 mg dL (2 pts) Which of the following is correct Explain why s 50 mg dL ii 50 mg dL (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

The Answer is in the image, click to view ...

Answered step by step

Verified Expert Solution

Link Copied!

Question

1 Approved Answer

Posted on Jun 29, 2024

Question 1 (2 points) (1 pt) For a standard normal distribution Z ~ N(0,1) what is the value for the quantile q that leaves 10%

Question 1 (2 points)

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

Question 2 (6 points)

(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 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?
(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.

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

(2 pts) Which of the following is correct? Explain why.
1. = 195 mg/dL ii. = 195 mg/dL
(2 pts) Which of the following is correct? Explain why.
1. s = 50 mg/dL ii. = 50 mg.dL
(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.