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**Understanding Glucose Levels and Probability Distributions** **Overview:** Let *x* be a random variable representing the level of glucose in the blood (measured in milligrams per deciliter) after a 12-hour fast. For individuals under 50 years old, *x* is approximately normally distributed with a mean (μ) of 70 and a standard deviation (σ) of 39. A test result of *x* < 40 indicates severe excess insulin, warranting medication. **Exercises:** **(a) Probability of Single Test Result:** - **Question:** What is the probability that, in a single test, *x* < 40? - **Answer:** 0.2209 ✔️ **(b) Probability Distribution for Averaged Tests:** - Suppose a doctor uses the average (x̄) for two tests taken about a week apart. What can we say about the probability distribution of x̄? - **Options:** 1. The distribution of x̄ is approximately normal with μx̄ = 70 and σx̄ = 27.58. 2. The distribution of x̄ is not normal. 3. The distribution of x̄ is approximately normal with μx̄ = 70 and σx̄ = 39. 4. The distribution of x̄ is approximately normal with μx̄ = 70 and σx̄ = 19.50. ✔️ - **Question:** What is the probability that x̄ < 40? - **Answer:** 0.1379 ✔️ **(c) Probability for n = 3 Tests:** - Repeat part (b) for n = 3 tests taken a week apart. - **Incorrect attempt:** 22.5160 ✖️ **(d) Probability for n = 5 Tests:** - Repeat part (b) for n = 5 tests taken a week apart. - **Answer:** 0.0918 ✔️ **Note:** This exercise helps understand the effect of the number of tests on the standard deviation and the probability outcome, applying concepts from normal distribution and the central limit theorem.

**Understanding Glucose Levels and Probability Distributions** **Overview:** Let *x* be a random variable representing the level of glucose in the blood (measured in milligrams per deciliter) after a 12-hour fast. For individuals under 50 years old, *x* is approximately normally distributed with a mean (μ) of 70 and a standard deviation (σ) of 39. A test result of *x* < 40 indicates severe excess insulin, warranting medication. **Exercises:** **(a) Probability of Single Test Result:** - **Question:** What is the probability that, in a single test, *x* < 40? - **Answer:** 0.2209 ✔️ **(b) Probability Distribution for Averaged Tests:** - Suppose a doctor uses the average (x̄) for two tests taken about a week apart. What can we say about the probability distribution of x̄? - **Options:** 1. The distribution of x̄ is approximately normal with μx̄ = 70 and σx̄ = 27.58. 2. The distribution of x̄ is not normal. 3. The distribution of x̄ is approximately normal with μx̄ = 70 and σx̄ = 39. 4. The distribution of x̄ is approximately normal with μx̄ = 70 and σx̄ = 19.50. ✔️ - **Question:** What is the probability that x̄ < 40? - **Answer:** 0.1379 ✔️ **(c) Probability for n = 3 Tests:** - Repeat part (b) for n = 3 tests taken a week apart. - **Incorrect attempt:** 22.5160 ✖️ **(d) Probability for n = 5 Tests:** - Repeat part (b) for n = 5 tests taken a week apart. - **Answer:** 0.0918 ✔️ **Note:** This exercise helps understand the effect of the number of tests on the standard deviation and the probability outcome, applying concepts from normal distribution and the central limit theorem.

MATLAB: An Introduction with Applications
MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
Section: Chapter Questions
Problem 1P
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**Understanding Glucose Levels and Probability Distributions** **Overview:** Let *x* be a random variable representing the level of glucose in the blood (measured in milligrams per deciliter) after a 12-hour fast. For individuals under 50 years old, *x* is approximately normally distributed with a mean (μ) of 70 and a standard deviation (σ) of 39. A test result of *x* < 40 indicates severe excess insulin, warranting medication. **Exercises:** **(a) Probability of Single Test Result:** - **Question:** What is the probability that, in a single test, *x* < 40? - **Answer:** 0.2209 ✔️ **(b) Probability Distribution for Averaged Tests:** - Suppose a doctor uses the average (x̄) for two tests taken about a week apart. What can we say about the probability distribution of x̄? - **Options:** 1. The distribution of x̄ is approximately normal with μx̄ = 70 and σx̄ = 27.58. 2. The distribution of x̄ is not normal. 3. The distribution of x̄ is approximately normal with μx̄ = 70 and σx̄ = 39. 4. The distribution of x̄ is approximately normal with μx̄ = 70 and σx̄ = 19.50. ✔️ - **Question:** What is the probability that x̄ < 40? - **Answer:** 0.1379 ✔️ **(c) Probability for n = 3 Tests:** - Repeat part (b) for n = 3 tests taken a week apart. - **Incorrect attempt:** 22.5160 ✖️ **(d) Probability for n = 5 Tests:** - Repeat part (b) for n = 5 tests taken a week apart. - **Answer:** 0.0918 ✔️ **Note:** This exercise helps understand the effect of the number of tests on the standard deviation and the probability outcome, applying concepts from normal distribution and the central limit theorem.
Transcribed Image Text:**Understanding Glucose Levels and Probability Distributions** **Overview:** Let *x* be a random variable representing the level of glucose in the blood (measured in milligrams per deciliter) after a 12-hour fast. For individuals under 50 years old, *x* is approximately normally distributed with a mean (μ) of 70 and a standard deviation (σ) of 39. A test result of *x* < 40 indicates severe excess insulin, warranting medication. **Exercises:** **(a) Probability of Single Test Result:** - **Question:** What is the probability that, in a single test, *x* < 40? - **Answer:** 0.2209 ✔️ **(b) Probability Distribution for Averaged Tests:** - Suppose a doctor uses the average (x̄) for two tests taken about a week apart. What can we say about the probability distribution of x̄? - **Options:** 1. The distribution of x̄ is approximately normal with μx̄ = 70 and σx̄ = 27.58. 2. The distribution of x̄ is not normal. 3. The distribution of x̄ is approximately normal with μx̄ = 70 and σx̄ = 39. 4. The distribution of x̄ is approximately normal with μx̄ = 70 and σx̄ = 19.50. ✔️ - **Question:** What is the probability that x̄ < 40? - **Answer:** 0.1379 ✔️ **(c) Probability for n = 3 Tests:** - Repeat part (b) for n = 3 tests taken a week apart. - **Incorrect attempt:** 22.5160 ✖️ **(d) Probability for n = 5 Tests:** - Repeat part (b) for n = 5 tests taken a week apart. - **Answer:** 0.0918 ✔️ **Note:** This exercise helps understand the effect of the number of tests on the standard deviation and the probability outcome, applying concepts from normal distribution and the central limit theorem.
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