A study is conducted to investigate how contracting a certain disease may affect the blood sugar levels 2 hours after meal. It is found that about 10% of the patients with the disease have blood sugar levels over 7.28 mmol/L; about 4% of the patients with the disease have blood sugar levels below 4.25 mmol/L. Suppose the blood sugar levels are normally distributed. (a) Find the mean and standard deviation of the blood sugar levels for patients with the disease. (b) If patients are examined one after another, what is the probability that the 10th patient is the 6th one with blood sugar level between 4.25 mmol/L and 7.28 mmol/L? (c) Randomly select 20 patients. How many of them are expected to have blood sugar level between 4.25 mmol/L and 7.28 mmol/L? (d) Randomly select 20 patients. Find the probability that their average blood sugar level is above 6.12 mmol/L.
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Throwback question: In pharmacologic research a variety of clinical chemistry measurements are routinely monitored closely for evidence of side effects of the medication under study. Suppose typical blood-glucose levels are normally distributed with mean 92.47 mg/dl and standard deviation 29.99 mg/dl. (Note: Round all of your answers to four decimal places where appropriate.) We would expect the blood glucose levels to fall between and in 99.7% of patients._______ A normal glucose range is 65 - 120 mg/dl. What is the probability a patient's blood glucose level falls between these two values? z1 = _____ z2 = _____ probability = _______ What is the probability that a patient's blood glucose level is greater than 52 mg/dl? z = ______ probability = ______ If a blood glucose level is in the top 2%, then the patient is classified as abnormal. What blood glucose level corresponds to this cut-off? z = ________ glucose =______ mg/dl
Ahmet Y.
17) Blood glucose levels in humans have a mean value, μ, of 80 and standard deviation, σ, of 10. The blood glucose levels of 35 random patients in a very large, metropolitan hospital are found. (Give 4 decimal places where appropriate.) a. Verify that the three conditions for the Central Limit Theorem for means are met. Give explanations, and be specific. b. Describe the sampling distribution (shape, center, spread) of the sample mean blood glucose level for the 35 patients. Use symbols where appropriate. c. Find the probability that the mean for the random sample is between 78 and 81. d. Suppose that the 35 random patients have a mean glucose level above 85, which is unusual with a probability of 0.0101. Give three different explanations for this result.
Danielle F.
Medical: Blood Glucose Let $x$ be a random variable that represents the level of glucose in the blood (milligrams per deciliter of blood) after a 12 -hour fast. Assume that for people under 50 years old, $x$ has a distribution that is approximately normal, with mean $\mu=85$ and estimated standard deviation $\sigma=25$ (based on information from Diagnostic Tests with Nursing Applications, edited by S. Loeb, Springhouse). A test result $x<40$ is an indication of severe excess insulin, and medication is usually prescribed. (a) What is the probability that, on a single test, $x<40 ?$ (b) Suppose a doctor uses the average $\bar{x}$ for two tests taken about a week apart. What can we say about the probability distribution of $x ?$ Hint: See Theorem $7.1 .$ What is the probability that $x < 40 ?$ (c) Repeat part (b) for $n=3$ tests taken a week apart. (d) Repeat part (b) for $n=5$ tests taken a week apart. (e) Interpretation Compare your answers to parts $(a),(b),(c),$ and $(d)$. Did the probabilities decrease as $n$ increased? Explain what this might imply if you were a doctor or a nurse. If $a$ patient had a test result of $\bar{x}<40$ based on five tests, explain why either you are looking at an extremely rare event or (more likely) the person has a case of excess insulin.
Estimation
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