document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1199759>Question 1199759</A>: <I><SPAN STYLE=\"word-break: break-all;\"> 62% of all Americans are home owners. If 35 Americans are randomly selected, find the probability that\r<BR>\n" );
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document.write( "a. Exactly 22 of them are are home owners. \r<BR>\n" );
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document.write( "b. At most 24 of them are are home owners. \r<BR>\n" );
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document.write( "c. At least 22 of them are home owners. \r<BR>\n" );
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document.write( "d. Between 17 and 21 (including 17 and 21) of them are home owners. <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 #848247 by </B><A HREF=/tutors/aboutme.mpl?userid=textot><B>textot(100)</B></A><img src=\"/images/stars/stars-08.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=textot><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=848247\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> **a. Probability of exactly 22 homeowners:**\r<BR>\n" );
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document.write( "* This follows a binomial distribution with:<BR>\n" );
document.write( "    * n = 35 (sample size)<BR>\n" );
document.write( "    * p = 0.62 (probability of success - homeowner)<BR>\n" );
document.write( "    * q = 1 - p = 0.38 (probability of failure - not a homeowner)<BR>\n" );
document.write( "    * k = 22 (number of successes)\r<BR>\n" );
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document.write( "* Using the binomial probability formula:<BR>\n" );
document.write( "   P(X = k) = (nCk) * p^k * q^(n-k) <BR>\n" );
document.write( "   where nCk = n! / (k! * (n-k)!)\r<BR>\n" );
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document.write( "* P(X = 22) = (35C22) * (0.62)^22 * (0.38)^(35-22) <BR>\n" );
document.write( "   P(X = 22) ≈ 0.0898\r<BR>\n" );
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document.write( "**b. Probability of at most 24 homeowners:**\r<BR>\n" );
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document.write( "* P(X ≤ 24) = P(X = 0) + P(X = 1) + ... + P(X = 24)\r<BR>\n" );
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document.write( "* This requires calculating the binomial probability for each value of X from 0 to 24 and summing them. \r<BR>\n" );
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document.write( "* Using a calculator or statistical software (like Excel or a TI-84 calculator with the binomcdf function):<BR>\n" );
document.write( "   P(X ≤ 24) ≈ 0.9588\r<BR>\n" );
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document.write( "**c. Probability of at least 22 homeowners:**\r<BR>\n" );
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document.write( "* P(X ≥ 22) = P(X = 22) + P(X = 23) + ... + P(X = 35)\r<BR>\n" );
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document.write( "* This requires calculating the binomial probability for each value of X from 22 to 35 and summing them.\r<BR>\n" );
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document.write( "* Alternatively:<BR>\n" );
document.write( "   P(X ≥ 22) = 1 - P(X ≤ 21)\r<BR>\n" );
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document.write( "* Using a calculator or statistical software:<BR>\n" );
document.write( "   P(X ≥ 22) ≈ 0.2493\r<BR>\n" );
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document.write( "**d. Probability of between 17 and 21 homeowners (inclusive):**\r<BR>\n" );
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document.write( "* P(17 ≤ X ≤ 21) = P(X = 17) + P(X = 18) + ... + P(X = 21)\r<BR>\n" );
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document.write( "* Calculate each probability using the binomial probability formula and sum them up.\r<BR>\n" );
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document.write( "* Using a calculator or statistical software:<BR>\n" );
document.write( "   P(17 ≤ X ≤ 21) ≈ 0.6550\r<BR>\n" );
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document.write( "**In summary:**\r<BR>\n" );
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document.write( "* a) Probability of exactly 22 homeowners: 0.0898<BR>\n" );
document.write( "* b) Probability of at most 24 homeowners: 0.9588<BR>\n" );
document.write( "* c) Probability of at least 22 homeowners: 0.2493<BR>\n" );
document.write( "* d) Probability of between 17 and 21 homeowners: 0.6550<BR>\n" );
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