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Ch. 6 - Normal Probability Distributions
Triola - Elementary Statistics 14th Edition
Triola14th EditionElementary StatisticsISBN: 9780137366446Non è quello che usi tu?Cambia libro di testo
Tutti i libri di testoTriola 14th EditionCh. 6 - Normal Probability DistributionsProblema 6.1.5
Capitolo 6, Problema 6.1.5

Continuous Uniform Distribution. In Exercises 5–8, refer to the continuous uniform distribution depicted in Figure 6-2 and described in Example 1. Assume that a passenger is randomly selected, and find the probability that the waiting time is within the given range.


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Greater than 3.00 minutes

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Identify the type of distribution: The problem involves a continuous uniform distribution, which is defined by a constant probability density function (PDF) over a specific interval. From the graph, the interval is [0, 5] and the height of the PDF is 0.2.
Recall the formula for the probability in a continuous uniform distribution: The probability of an event occurring within a range [a, b] is given by the formula P(a ≤ X ≤ b) = (b - a) * height of the PDF.
Determine the range of interest: The problem asks for the probability that the waiting time is greater than 3.00 minutes. This corresponds to the range [3, 5].
Substitute the values into the formula: Use the formula P(a ≤ X ≤ b) = (b - a) * height. Here, a = 3, b = 5, and the height of the PDF is 0.2. Substitute these values into the formula.
Simplify the expression: Perform the subtraction (b - a) and multiply the result by the height of the PDF to find the probability. This will give you the final answer.

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Continuous Uniform Distribution

A continuous uniform distribution is a probability distribution where all outcomes are equally likely within a specified range. The probability density function (PDF) is constant across this interval, meaning that the likelihood of any specific value is the same. In the context of waiting times, this distribution can be used to model scenarios where the waiting time is uniformly distributed between a minimum and maximum value.
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Intro to Frequency Distributions

Probability Density Function (PDF)

The probability density function (PDF) describes the likelihood of a continuous random variable taking on a specific value. For a continuous uniform distribution, the PDF is a horizontal line, indicating that the probability is evenly distributed across the range. The area under the PDF curve represents the total probability, which equals 1, and the height of the line is determined by the range of values.
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Introduction to Probability

Calculating Probabilities

To find the probability of a continuous random variable falling within a certain range, one must calculate the area under the PDF over that interval. For the continuous uniform distribution, this is done by multiplying the height of the PDF by the width of the interval. For example, to find the probability that the waiting time is greater than 3 minutes, one would calculate the area from 3 to the maximum value of the distribution.
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Probability From Given Z-Scores - TI-84 (CE) Calculator
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Pulse Rates. In Exercises 13–24, use the data in the table below for pulse rates of adult males and females (based on Data Set 1 “Body Data” in Appendix B). Hint: Draw a graph in each case.


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Find the probability that a male has a pulse rate between 70 beats per minute and 90 beats per minute.

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Satisfying Requirements Data Set 1 “Body Data” in Appendix B includes a sample of 147 pulse rates of randomly selected women. Does that sample satisfy the following requirement: (1) The sample appears to be from a normally distributed population; or (2) the sample has a size of n>30?

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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, then find the probability of the given bone density test scores. If using technology instead of Table A-2, round answers to four decimal places.


Less than -2.00

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Pulse Rates. In Exercises 13–24, use the data in the table below for pulse rates of adult males and females (based on Data Set 1 “Body Data” in Appendix B). Hint: Draw a graph in each case.


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For males, find P90 which is the pulse rate separating the bottom 90% from the top 10%.

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IQ Scores. In Exercises 5–8, find the area of the shaded region. The graphs depict IQ scores of adults, and those scores are normally distributed with a mean of 100 and a standard deviation of 15 (as on the Wechsler IQ test).

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Interpreting Normal Quantile Plots. In Exercises 5–8, examine the normal quantile plot and determine whether the sample data appear to be from a population with a normal distribution.


Ages of Presidents The normal quantile plot represents the ages of presidents of the United States at the times of their inaugurations. The data are from Data Set 22 “Presidents” in Appendix B.

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