document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=67265>Question 67265</A>: <I><SPAN STYLE=\"word-break: break-all;\"> 1. The average yearly cost per household of owning a dog is $186.80.  Suppose that we randomly select 50 households that own a dog.  What is the probability that the sample mean for these 50 households is less than $175.00.<BR>\n" );
document.write( "Assume o = $32<BR>\n" );
document.write( "z =X - u/o \r<BR>\n" );
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document.write( "z = 175.00- 186.80/32 = -11.8/32 = -3.6875 <BR>\n" );
document.write( "   0.5000-0.1406 = 0.6406<BR>\n" );
document.write( "  P(X < 175) =  0.6406 = 64%  (not sure if used correct steps)\r<BR>\n" );
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document.write( "b.  Sample Mean - mean/ standard deviation/ square root of N.\r<BR>\n" );
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document.write( "175 - 186.80 / 32/(squqare root of 50 = -2.607<BR>\n" );
document.write( "0.5000 +4955 = .9955 = 99% or 100%\r<BR>\n" );
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document.write( "2.  The average teacher’s salary in North Dakota is $29863.  Assume a normal distribution with &#61555; = $5100.<BR>\n" );
document.write( "a. What is the probability that a randomly selected teacher’s salary is greater than $40,000?<BR>\n" );
document.write( "b. What is the probability that the mean for a sample of 80 teachers’ salaries is greater than $30,000<BR>\n" );
document.write( "a.<BR>\n" );
document.write( "z = 29863 - 40000/5100 = -10137/5100 = -1.98  0.5000+.4761 = .9761 = 98%<BR>\n" );
document.write( " P(X>40,000)\r<BR>\n" );
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document.write( "3.  For a certain year the average annual salary in Pennsylvania was $24,393.  Assume that salaries were normally distributed for a certain group of wage earners, and the standard deviation of this group was $4362.\r<BR>\n" );
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document.write( "a. Find the probability that randomly selected individual earned less than $26,000.<BR>\n" );
document.write( "b. Find the probability that, for a randomly selected sample of 25 individuals, the mean salary was less than $26,000.<BR>\n" );
document.write( "c. Why is the probability for Part b higher than the probability for Part a?\r<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 #47853 by </B><A HREF=/tutors/aboutme.mpl?userid=stanbon><B>stanbon(75887)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=stanbon><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=47853\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> 1. The average yearly cost per household of owning a dog is $186.80.  Suppose that we randomly select 50 households that own a dog.  What is the probability that the sample mean for these 50 households is less than $175.00.<BR>\n" );
document.write( "Assume o = $32<BR>\n" );
document.write( "z =X - u/o <BR>\n" );
document.write( "COMMENT: If sigma=$32 , s=32/sqrt50 (this is the std dev of the sample means)<BR>\n" );
document.write( "z = [175.00- 186.80]/[32sqrt50] = -11.8/4.525 = -2.607<BR>\n" );
document.write( "  P(z<-2.607)=0.004567<BR>\n" );
document.write( "  P(X < 175) =  0.4%\r<BR>\n" );
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document.write( "b.  Sample Mean - mean/ standard deviation/ square root of N.\r<BR>\n" );
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document.write( "COMMENT: You have it right below.<BR>\n" );
document.write( "175 - 186.80 / 32/(square root of 50 = -2.607<BR>\n" );
document.write( "But you want P(z<-2.607) which is approx 0.4%<BR>\n" );
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document.write( "2.  The average teacher’s salary in North Dakota is $29863.  Assume a normal distribution with sigma = $5100.<BR>\n" );
document.write( "a. What is the probability that a randomly selected teacher’s salary is greater than $40,000?<BR>\n" );
document.write( "b. What is the probability that the mean for a sample of 80 teachers’ salaries is greater than $30,000<BR>\n" );
document.write( "a.<BR>\n" );
document.write( "COMMENT: You want the z-value of 40,000.  You need to switch your numbers.<BR>\n" );
document.write( "z(40,000) = (40000-29863)/5100 = 10137/5100 = 1.98  <BR>\n" );
document.write( " P(X>40,000)=P(z>1.98)=0.0239 or appox 2.4%<BR>\n" );
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document.write( "3.  For a certain year the average annual salary in Pennsylvania was $24,393.  Assume that salaries were normally distributed for a certain group of wage earners, and the standard deviation of this group was $4362.\r<BR>\n" );
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document.write( "a. Find the probability that randomly selected individual earned less than $26,000.<BR>\n" );
document.write( "COMMENT: Find the z of 26000<BR>\n" );
document.write( "z(26000)=[26000-24393]/4362=0.3684<BR>\n" );
document.write( "P(z<0.3684)=0.6437... or appox 64.4%<BR>\n" );
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document.write( "b. Find the probability that, for a randomly selected sample of 25 individuals, the mean salary was less than $26,000.<BR>\n" );
document.write( "COMMENT: Here you have to change the std dev to 24393/sqrt(25)<BR>\n" );
document.write( "c. Why is the probability for Part b higher than the probability for Part a?<BR>\n" );
document.write( "COMMENT: The standard deviation is smaller resulting in a higher z-value<BR>\n" );
document.write( "and therefore more population or probability below that z value.<BR>\n" );
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document.write( "Cheers,<BR>\n" );
document.write( "Stan<BR>\n" );
document.write( "PS: If you have more stat questions as you go through your course I would<BR>\n" );
document.write( "be happy to help you.  I am looking for an opportunity to review what I <BR>\n" );
document.write( "know about stat.  You may email me directly at stanbon@comcast.net\r<BR>\n" );
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