document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1159593>Question 1159593</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Please help me solve these.. I am having such a hard time. \r<BR>\n" );
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document.write( "A baseball player has a batting average of 0.245. What is the probability that he has exactly 4 hits in his next 7 at bats?\r<BR>\n" );
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document.write( "The results of a common standardized test used in psychology research is designed so that the population mean is 165 and the standard deviation is 20. A subject earns a score of 217. What is the z-score for this raw score?<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 #782666 by </B><A HREF=/tutors/aboutme.mpl?userid=jim_thompson5910><B>jim_thompson5910(35256)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=jim_thompson5910><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=782666\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <font color=black size=3><BR>\n" );
document.write( "Problem 1\r<BR>\n" );
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document.write( "p = 0.245 is the probability of success = probability of getting a hit<BR>\n" );
document.write( "k = number of hits we want = 4<BR>\n" );
document.write( "n = sample size = number of at bats (aka batting attempts) = 7\r<BR>\n" );
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document.write( "Compute the binomial coefficient<BR>\n" );
document.write( "Use the combination formula<BR>\n" );
document.write( "n C k = (n!)/(k!*(n-k)!)<BR>\n" );
document.write( "7 C 4 = (7!)/(4!*(7-4)!)<BR>\n" );
document.write( "7 C 4 = (7!)/(4!*3!)<BR>\n" );
document.write( "7 C 4 = (7*6*5*4!)/(4!*3!)<BR>\n" );
document.write( "7 C 4 = (7*6*5)/(3!)<BR>\n" );
document.write( "7 C 4 = (7*6*5)/(3*2*1)<BR>\n" );
document.write( "7 C 4 = 210/6<BR>\n" );
document.write( "7 C 4 = 35\r<BR>\n" );
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document.write( "This is then useful to compute the binomial probability <BR>\n" );
document.write( "P(X = k) = (n C k)*(p)^(k)*(1-p)^(n-k)<BR>\n" );
document.write( "P(X = 4) = (7 C 4)*(0.245)^(4)*(1-0.245)^(7-4)<BR>\n" );
document.write( "P(X = 4) = (7 C 4)*(0.245)^(4)*(0.755)^(3)<BR>\n" );
document.write( "P(X = 4) = (35)*(0.245)^(4)*(0.755)^3<BR>\n" );
document.write( "P(X = 4) = (35)*(0.003603000625)*(0.430368875)<BR>\n" );
document.write( "P(X = 4) = 0.0542716763961941\r<BR>\n" );
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document.write( "You didnt provide rounding instructions, so make sure you check with the teacher to see how many decimal places they want for the final answer. If they wanted say 3 decimal places, then 0.0542716763961941 rounds to 0.054\r<BR>\n" );
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document.write( "So there's roughly a 5.4% chance of the player hitting exactly 4 times out of 7 attempts at bat. \r<BR>\n" );
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document.write( "Problem 2\r<BR>\n" );
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document.write( "x = 217 is the raw score<BR>\n" );
document.write( "mu = 165 is the population mean<BR>\n" );
document.write( "sigma = 20 is the population standard deviation\r<BR>\n" );
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document.write( "Plug those values into the formula below.<BR>\n" );
document.write( "z = (x-mu)/sigma<BR>\n" );
document.write( "z = (217-165)/20<BR>\n" );
document.write( "z = 52/20<BR>\n" );
document.write( "z = 2.6\r<BR>\n" );
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document.write( "The z score is 2.6<BR>\n" );
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