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Standard Normal Distribution. In Exercises, | Ch 6.2 - 28BSC

Elementary Statistics | 12th Edition | ISBN: 9780321836960 | Authors: Mario F. Triola ISBN: 9780321836960 18

Solution for problem 28BSC Chapter 6.2

Elementary Statistics | 12th Edition

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Elementary Statistics | 12th Edition | ISBN: 9780321836960 | Authors: Mario F. Triola

Elementary Statistics | 12th Edition

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Problem 28BSC

Standard Normal Distribution. In Exercises 17–36, assume that a randomly selected subject is given a bone density test. Those test scores are normally distributed with a mean of 0 and a standard deviation of 1. In each case, draw a graph and find the probability of the given scores. If using technology instead of Table A-2, round answers to four decimal places.

Between − 1.93 and − 0.45

Step-by-Step Solution:

Answer :

Step 1 :

In finding the area under standard normal curve, you can use the statistical tables at the back of your textbook, or use your calculator.

In using the tables, remember that areas are reported as P(Z < a)

Therefore, you need to use the following relationships

P(Z > a) = 1 - P(Z < a)

P(a < Z < b) = P(Z < b) - P(Z < a)

Applying this principles, we get

P(-1.93 < Z < -0.45) = P(Z < -0.45) - P(Z < -1.93)

Area under normal curve can be calculated by using standard normal table or statistical table that is

P(z < -0.45) = 0.3264 (i.e, row -0.4 under column 0.05)

   P(z < -1.93) = 0.0268(i.e, row -1.9 under column 0.03)

then

                                  = 0.3264 - 0.0268

                                   = 0.2996

Step 2 of 1

Chapter 6.2, Problem 28BSC is Solved
Textbook: Elementary Statistics
Edition: 12
Author: Mario F. Triola
ISBN: 9780321836960

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Standard Normal Distribution. In Exercises, | Ch 6.2 - 28BSC