document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1206571>Question 1206571</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Use the probability distribution for the random variable x to answer the question.<BR>\n" );
document.write( "x	0	1	2	3	4	5<BR>\n" );
document.write( "p(x)<BR>\n" );
document.write( "0.35	0.2	0.19	0.17	0.06	0.03<BR>\n" );
document.write( "Locate the interval <BR>\n" );
document.write( "𝜇 ± 2𝜎<BR>\n" );
document.write( " on the x-axis of a probability histogram. You are given that the mean is 1.48 and the standard deviation is 1.42. What is the probability that x will fall into this interval?<BR>\n" );
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document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #844132 by </B><A HREF=/tutors/aboutme.mpl?userid=math_tutor2020><B>math_tutor2020(3817)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=math_tutor2020><IMG SRC=http://www.algebra.com/images/aboutme-small.gif BORDER=0 alt=\"About Me\" VALIGN=MIDDLE></A>&nbsp;<IMG SRC=http://www.algebra.com/images/nopicture.jpg><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=844132\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <font color=black size=3><BR>\n" );
document.write( "𝜇 = greek letter mu = mean = 1.48<BR>\n" );
document.write( "𝜎 = greek letter sigma = standard deviation = 1.42\r<BR>\n" );
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document.write( "𝜇 ± 2𝜎 breaks down into 𝜇 - 2𝜎 and 𝜇 + 2𝜎\r<BR>\n" );
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document.write( "This will mean 𝜇 - 2𝜎 < x < 𝜇 + 2𝜎\r<BR>\n" );
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document.write( "𝜇 - 2𝜎 = 1.48 - 2*1.42 = -1.36<BR>\n" );
document.write( "𝜇 + 2𝜎 = 1.48 + 2*1.42 = 4.32\r<BR>\n" );
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document.write( "We're focused on the interval -1.36 < x < 4.32\r<BR>\n" );
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document.write( "If x is an integer then we focus on the sub-interval <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-1+%3C=+x+%3C=+4 ALIGN=MIDDLE  ALT=\"-1+%3C=+x+%3C=+4\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Furthermore, the smallest x can be in this case is x = 0, so we're really only going to focus on <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=0+%3C=+x+%3C=+4 ALIGN=MIDDLE  ALT=\"0+%3C=+x+%3C=+4\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Add up the probability values associated with x = 0 through x = 4.<BR>\n" );
document.write( "P(0)+P(1)+P(2)+P(4) = 0.35+0.2+0.19+0.17+0.06 = <font color=red>0.97</font> which is the final answer\r<BR>\n" );
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document.write( "Or as an alternate route<BR>\n" );
document.write( "P(5) = 0.03<BR>\n" );
document.write( "P(value between 0 and 4) = 1 - P(5) = 1 - 0.03 = <font color=red>0.97</font>\r<BR>\n" );
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document.write( "There's a 97% chance of picking an x value between 0 and 4 inclusive of both endpoints. <BR>\n" );
document.write( "This is equivalent to saying there's a 97% chance of picking an x value such that -1.36 < x < 4.32; where each endpoint is two standard deviations away from the mean.\r<BR>\n" );
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document.write( "Answer: <font color=red>0.97</font><BR>\n" );
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