Answered: The systolic blood pressure of adults…

A First Course in Probability (10th Edition)

10th Edition

ISBN:9780134753119

Author:Sheldon Ross

Publisher:Sheldon Ross

Chapter1: Combinatorial Analysis

Section: Chapter Questions

Problem 1.1P: a. How many different 7-place license plates are possible if the first 2 places are for letters and...

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The systolic blood pressure of adults in the USA is nearly normally distributed with a mean of 120 and standard deviation of 24 .
Someone qualifies as having Stage 2 high blood pressure if their systolic blood pressure is 160 or higher.

a. Around what percentage of adults in the USA have stage 2 high blood pressure?

b. If you sampled 2000 people, how many would you expect to have BP> 160? Give your answer to the nearest person.
people

c. Stage 1 high BP is specified as systolic BP between 140 and 160. What percentage of adults in the US qualify for stage 1?

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 + ...

Expert Solution

Step 1

Given Information:

Mean $μ$ = 120

Standard deviation $σ$ = 24

Someone qualifies as having Stage 2 high blood pressure if their systolic blood pressure is $\geq 160$ .

(a) To find the percentage of adults in the USA who have stage 2 high blood pressure:

Z-score is a measure which tells how many standard deviations away, a data value is, from the mean. It is given by the formula:

$Z = \frac{X - μ}{σ}$

Required probability is given as:

$\begin{array}{rcl} P (X \geq 160) & = & 1 - P (X < 160) \\ = & 1 - P (\frac{X - μ}{σ} < \frac{160 - 120}{24}) \\ = & 1 - P (Z < 1.67) \\ = & 1 - 0.95254 [U \sin g s \tan d a r d n o r m a l t a b l e] \\ = & 0.04746 \end{array}$

Using a standard normal table, look up for z-score 1.67 i.e., 1.6 in the row and 0.07 along the column, the intersection of both values gives a probability of 0.95254. Then, subtract the value from total probability 1. (Since, standard normal table, gives area to the left of z-score and we want area to the right)

Therefore, percentage of adults in the USA who have stage 2 high blood pressure is 4.746%

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