**Understanding Probability Distributions and the Central Limit Theorem**In the United States, the systolic blood pressure of a randomly selected patient follows a normal distribution with a mean (µ) of 116 mmHg and a standard deviation (σ) of 15.5 mmHg. Let \( X \) represent the systolic blood pressure of a randomly selected patient, and let \( \overline{X} \) represent the average systolic blood pressure of a random sample of size 22.1. **Probability Distribution of \( X \)** - Describe the probability distribution of \( X \) and specify its parameters \( \mu \) and \( \sigma \): \( X \sim N(\mu = 116, \sigma = 15.5) \) - Calculate the probability that the systolic blood pressure of a randomly selected patient is more than 121.9 mmHg. (Round the answer to 4 decimal places)2. **Using the Central Limit Theorem** - Apply the Central Limit Theorem to describe the probability distribution of \( \overline{X} \) and specify its parameters \( \mu_{\overline{X}} \) and \( \sigma_{\overline{X}} \): \( \overline{X} \sim N(\mu_{\overline{X}} = 116, \sigma_{\overline{X}} = 3.306) \) - Calculate the probability that the average systolic blood pressure of a sample of 22 randomly selected patients is between 117.4 and 121.5 mmHg. (Round the answer to 4 decimal places)In this module, students will learn how to determine and describe probability distributions, as well as apply the Central Limit Theorem to understand sample means. Students will also practice calculating probabilities associated with these distributions.

The population mean is 116 and the population standard deviation is 15.5.

Answered: In the US, the systolic blood pressure…

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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Assume that the amount of weight that male college students gain during their freshman year are normally distributed with a. Mean of u= 1.2 kg and a standard deviation of o= 5.1 kg A. If 1 male college student is randomly selected, Find the probability that he gains between 0 and 3 kg during freshman year B. If 25 male college students are randomly selected find the probability that their mean weight gain during freshman year is between 0 and 3 kg why can the normal distribution be used on pet b even though the sample size does not exceed 30?
According to USPS study, the weights of shipment packages are normally distributed with a mean of 20.7 oz and a standard deviation of 4 oz. Let X be the weight of a randomly selected package. 1. Describe the probability distribution of X and state its parameters μ and σ: X ~ Correct ( μ= , σ= ) 2. Find the probability that the weight of a randomly selected package is less than 13 oz. (Round the answer to 4 decimal places) between 16 and 24 oz. (Round the answer to 4 decimal places) more than 27 oz. (Round the answer to 4 decimal places) 3. Find the 80-th percentile for the weights of shipment packages. oz (Round the answer to 1 decimal place)
In the US, the systolic blood pressure of a randomly selected patient is normally distributed with a mean of 120 mmHg and a standard deviation of 16.1 mmHg. Let X be the systolic blood pressure of a randomly selected patient and let X be the average systolic blood pressure of a random sample of size 14. 1. Describe the probability distribution of X and state its parameters μ and σ: or (μ= 12✓ and find the probability that the systolic blood pressure of a randomly selected patient is less than 85.2 mmHg. X~N X~ N 2 (Round the answer to 4 decimal places) 2. Use the Central Limit Theorem the original population is normally distributed although the sample size is small (n X 4. and find the probability that the average systolic blood pressure of a sample of 14 randomly selected patients is between 110.3 and 111 mmHg. 0.0 (Round the answer to 4 decimal places)
Let X be a random variable that represents the level of glucose in the blood (milligrams per deciliter of blood). The distribution of X for a healthy person is normally distributed with men u = 85 and standard deviation o = 25. A person suffers from severe excess in insulin would have a lower level of glucose. A blood test with result of X < 40 would be used as an indicator that medication is needed. (a) What is the probability that a healthy person will be suggested with medication after a single test? (b) A doctor uses the average result of 2 tests for diagnosis, that is X. The second test will be conducted one week after the first test, so that the two test results are independent. For many healthy persons, each has finished two tests, find the expectation and standard error of the distribution of X. (c) The doctor suggests medication will be given only when the average level of glucoses in the 2 blood tests is less than 40, that is X < 40, so to reduce the chance of…
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The mean total cholesterol for a population of men between the ages of 20 and 29 is 180 micrograms per decilitre with a standard deviation of 37.4. A healthy total cholesterol level is less than 200, 200-240 is border line, and above 240 is dangerous. Assume the distribution is approximately Normal. For a randomly selected man from this group, what is the probability that his total cholesterol level is i. 200 or more? 1i. Between 200 and 240?
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