document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=510932>Question 510932</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Ok, These 6 problems I apparently did wrong on my test... Can someone do them and explain them a bit please?\r<BR>\n" );
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document.write( "1. A set of 50 data values has a mean of 28 and a variance of 4. <BR>\n" );
document.write( "a. Find the standard score (z) for a data value = 31. <BR>\n" );
document.write( "b. Find the probability of a data value > 31. \r<BR>\n" );
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document.write( "2.Find the area under the standard normal curve: <BR>\n" );
document.write( "a. to the right of z = 2.37 <BR>\n" );
document.write( "b. to the left of z = 2.37 \r<BR>\n" );
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document.write( "3. Assume that the population of heights of female college students is approximately normally distributed with mean m of 67 inches and standard deviation s of 3.95 inches. Show all work. <BR>\n" );
document.write( "(A) Find the proportion of female college students whose height is greater than 63 inches. <BR>\n" );
document.write( "(B) Find the proportion of female college students whose height is no more than 63 inches. \r<BR>\n" );
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document.write( "4. The diameters of grapefruits in a certain orchard are normally distributed with a mean of 6.45 inches and a standard deviation of 0.45 inches. Show all work. <BR>\n" );
document.write( "(A) What percentage of the grapefruits in this orchard have diameters less than 7.1 inches? <BR>\n" );
document.write( "(B) What percentage of the grapefruits in this orchard are larger than 6.8 inches? \r<BR>\n" );
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document.write( "5. Find the normal approximation for the binomial probability that x = 4, where n = 13 and p = 0.3. Compare this probability to the value of P(x=5) found in Table 2 of Appendix B in your textbook. \r<BR>\n" );
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document.write( "6. A set of data is normally distributed with a mean of 100 and standard deviation of 15. · What would be the standard score for a score of 70? · What percentage of scores is between 100 and 70? · What would be the percentile rank for a score of 70? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #341993 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=341993\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> 1. A set of 50 data values has a mean of 28 and a variance of 4. <BR>\n" );
document.write( "a. Find the standard score (z) for a data value = 31.<BR>\n" );
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document.write( "z(31)= (31-28)/4 = 3/4<BR>\n" );
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document.write( "b. Find the probability of a data value > 31.<BR>\n" );
document.write( "P(x> 31) = P(z > 3/4) = 0.2266<BR>\n" );
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document.write( "2.Find the area under the standard normal curve: <BR>\n" );
document.write( "a. to the right of z = 2.37<BR>\n" );
document.write( "P(z > 2.37) = 0.0089<BR>\n" );
document.write( "---- <BR>\n" );
document.write( "b. to the left of z = 2.37<BR>\n" );
document.write( "P( z < 2.37) = 1 -0.0089 = 0.9911<BR>\n" );
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document.write( "3. Assume that the population of heights of female college students is approximately normally distributed with mean m of 67 inches and standard deviation s of 3.95 inches. Show all work. <BR>\n" );
document.write( "(A) Find the proportion of female college students whose height is greater than 63 inches.<BR>\n" );
document.write( "z(63) = (63-67)/3.95 = -1.0127<BR>\n" );
document.write( "P(x > 63) = P(z > -1.0127) = 0.8444<BR>\n" );
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document.write( "(B) Find the proportion of female college students whose height is no more than 63 inches.<BR>\n" );
document.write( "P(x <= 63) = 1-0.8444 = 0.1556<BR>\n" );
document.write( "================================================================= <BR>\n" );
document.write( "4. The diameters of grapefruits in a certain orchard are normally distributed with a mean of 6.45 inches and a standard deviation of 0.45 inches. Show all work. <BR>\n" );
document.write( "(A) What percentage of the grapefruits in this orchard have diameters less than 7.1 inches?<BR>\n" );
document.write( "Find the z-score of 7.1.<BR>\n" );
document.write( "Find the probability z is less than that z-score<BR>\n" );
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document.write( "(B) What percentage of the grapefruits in this orchard are larger than 6.8 inches? <BR>\n" );
document.write( "Follow the same procedure as in \"A\".<BR>\n" );
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document.write( "5. Find the normal approximation for the binomial probability that x = 4, where n = 13 and p = 0.3. Compare this probability to the value of P(x=5) found in Table 2 of Appendix B in your textbook.<BR>\n" );
document.write( "mean = np = 13*0.3 = 3.9<BR>\n" );
document.write( "s = sqrt(npq) = sqrt3.9*0.7) = 1.65<BR>\n" );
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document.write( "P( x = 4) = P(3.5 < x < 4.5)<BR>\n" );
document.write( "z(3.5) = (3.5-3.9)/1.65 = -0.2424<BR>\n" );
document.write( "z(4.5) = (4.5-3.9)/1.65 = 0.3636<BR>\n" );
document.write( "---<BR>\n" );
document.write( "P(x = 4) ~ P(-0.2424 < z < 0.3636) = 0.2377<BR>\n" );
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document.write( "Check your textbook for P(x = 4) = 0.2337<BR>\n" );
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document.write( "6. A set of data is normally distributed with a mean of 100 and standard deviation of 15.<BR>\n" );
document.write( "What would be the standard score for a score of 70? <BR>\n" );
document.write( "Find the z-score.<BR>\n" );
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document.write( "What percentage of scores is between 100 and 70? <BR>\n" );
document.write( "Find the z-scores and the percentage between them.<BR>\n" );
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document.write( "What would be the percentile rank for a score of 70?<BR>\n" );
document.write( "Find the z-score of 70; then find the percentage less than that z-score.<BR>\n" );
document.write( "Maybe round to a whole-number value.<BR>\n" );
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document.write( "Cheers,<BR>\n" );
document.write( "Stan H.<BR>\n" );
document.write( " </SPAN>\n" );
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