4. The glucose level of healthy adults is normally distributed with a mean of 100 mg/dL and a standard deviation of 10 mg/dL. One healthy adult is randomly selected. a) Find the probability that they have a glucose level less than 125 mg/dL. b) Find the probability that they have a glucose level more than 92 mg/dL. c) Find the probability that they have a glucose level between 88 mg/dL and 130 mg/dL d) A random sample of 300 healthy adults is collected. How many people in the sample do we expect to have a glucose level less than 125 mg/dL?
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Step 1: Calculate the probability that a randomly selected healthy adult has a glucose level less than 125 mg/dL. Show more…
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Glucose measurements for fasting adults are normally distributed with a mean of about 84.5 milligrams per deciliter (mg/dL) and a standard deviation of 7.25 mg/dL. If you randomly select a fasting adult, what is the probability that person's glucose measurement is: a) less than 70? b) between 72 and 82? c) higher than 99? Remember to show ALL work for finding the z-score AND what went into the calculator in normalcdf to get the final answer rounded correctly to 3 significant digits.
Adi S.
Madhur L.
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 $\bar{x} ?$ Hint: See Theorem $6.1 .$ What is the probability that $\bar{x}<40 ?$ (c) Repeat part (b) for $n=3$ tests taken a week apart. (d) Repeat part (b) for $n=5$ tests taken a week apart. (c) 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.
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