Answered: uess that the people reside in a city…

Glencoe Algebra 1, Student Edition, 9780079039897, 0079039898, 2018

18th Edition

ISBN:9780079039897

Author:Carter

Publisher:Carter

Chapter10: Statistics

Section10.4: Distributions Of Data

Problem 19PFA

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Question

Guess that the people reside in a city have a mean score of 50 and a standard deviation of 7 on a measure of concern about the environment. Assume that these scores are normally distributed.

1. If a person is randomly selected from that city then what is the probability that he or she has a score below 25?

b. If a person is randomly selected from that city then what is the probability that he or she has a score above 52?

c. If a person is randomly selected from that city then what is the probability that his/her score is between 30 and 40?

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

The provided information are:

Population mean ( $μ$ ) = 50

Population standard deviation ( $σ$ ) = 7

Step 2

Consider, X be the random variable that shows the scores is following the normal distribution with mean = 50 and standard deviation = 7.

(a)

The probability that randomly chosen person has score below 25 could be calculated as:

$\begin{array}{rcl} P (X & < & 25) = P (\frac{x - μ}{σ} < \frac{25 - μ}{σ}) \\ = & P (Z < \frac{25 - 50}{7}) \\ = & P (Z < - 3.57) \\ = & 0.0002 \end{array}$

Thus, the required probability is 0.0002.

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