 # Figure 511 the cumulative distribution function cdf

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Figure 5.11The cumulative distribution function (cdf) ofXis defined byP(Xx). It is a function ofxthat gives the probability thatthe random variable is less than or equal tox.FORMULA REVIEW5.1 Continuous Probability FunctionsProbability density function (pdf)f(x):f(x) ≥ 0The total area under the curvef(x) is one.Cumulative distribution function (cdf):P(Xx)PRACTICEChapter 5 | Continuous Random Variables201
5.1 Continuous Probability Functions1.Which type of distribution does the graph illustrate?Figure 5.122.Which type of distribution does the graph illustrate?Figure 5.133.Which type of distribution does the graph illustrate?Figure 5.14202Chapter 5 | Continuous Random VariablesThis OpenStax book is available for free at
4.What does the shaded area represent?P(___<x< ___)Figure 5.155.What does the shaded area represent?P(___<x< ___)Figure 5.166.For a continuous probablity distribution, 0 ≤x≤ 15. What isP(x> 15)?7.What is the area underf(x) if the function is a continuous probability density function?8.For a continuous probability distribution, 0 ≤x≤ 10. What isP(x= 7)?9.Acontinuousprobability function is restricted to the portion betweenx= 0 and 7. What isP(x= 10)?10.f(x) for a continuous probability function is15, and the function is restricted to 0 ≤x≤ 5. What isP(x< 0)?11.f(x), a continuous probability function, is equal to112, and the function is restricted to 0 ≤x≤ 12. What isP(0 <x<12)?Chapter 5 | Continuous Random Variables203
12.Find the probability thatxfalls in the shaded area.Figure 5.1713.Find the probability thatxfalls in the shaded area.Figure 5.1814.Find the probability thatxfalls in the shaded area.Figure 5.1915.f(x), a continuous probability function, is equal to13and the function is restricted to 1 ≤x≤ 4. DescribePx>32.HOMEWORK204Chapter 5 | Continuous Random VariablesThis OpenStax book is available for free at
5.1 Continuous Probability FunctionsFor each probability and percentile problem, draw the picture.16.Consider the following experiment. You are one of 100 people enlisted to take part in a study to determine the percentof nurses in America with an R.N. (registered nurse) degree. You ask nurses if they have an R.N. degree. The nursesanswer “yes” or “no.” You then calculate the percentage of nurses with an R.N. degree. You give that percentage to yoursupervisor.a.What part of the experiment will yield discrete data?b.What part of the experiment will yield continuous data?17.When age is rounded to the nearest year, do the data stay continuous, or do they become discrete?Why?SOLUTIONS1Uniform Distribution3Normal Distribution5P(6 <x< 7)7one9zero11one130.62515The probability is equal to the area fromx=32tox= 4 above the x-axis and up tof(x) =13.17Age is a measurement, regardless of the accuracy used.Chapter 5 | Continuous Random Variables205

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Probability distribution, probability density function
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