Answered: Suppose that systolic blood pressure is…

Algebra & Trigonometry with Analytic Geometry

13th Edition

ISBN:9781133382119

Author:Swokowski

Publisher:Swokowski

Chapter10: Sequences, Series, And Probability

Section: Chapter Questions

Problem 27T

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Question

Suppose that systolic blood pressure is approxiamtly Normally Distributed with a mean of 116 mmHg and a standard deviation of 21mmHg

We taken an SRS of 8 indivduals, measure their systolic blood pressure, and calcalate the sample mean.

A) Stage 2 hypertension is sometimes classified as 140mmHg or higher. What is the probability that the mean of a sample size of 8 is greater than 140 mmHg? Show all work.

B) If we repeated this many times, how many standard devations away from the mean would 70% of the sample means lie? Show your work.

C) Between which two values would the middle 70% of sample means lie? Show all work.

Definition Definition Measure of central tendency that is the average of a given data set. The mean value is evaluated as the quotient of the sum of all observations by the sample size. The mean, in contrast to a median, is affected by extreme values. Very large or very small values can distract the mean from the center of the data. Arithmetic mean: The most common type of mean is the arithmetic mean. It is evaluated using the formula: μ = 1 N ∑ i = 1 N x i Other types of means are the geometric mean, logarithmic mean, and harmonic mean. Geometric mean: The nth root of the product of n observations from a data set is defined as the geometric mean of the set: G = x 1 x 2 ... x n n Logarithmic mean: The difference of the natural logarithms of the two numbers, divided by the difference between the numbers is the logarithmic mean of the two numbers. The logarithmic mean is used particularly in heat transfer and mass transfer. ln x 2 − ln x 1 x 2 − x 1 Harmonic mean: The inverse of the arithmetic mean of the inverses of all the numbers in a data set is the harmonic mean of the data. 1 1 x 1 + 1 x 2 + ...

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