document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1120530>Question 1120530</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Max Scherzer, the starting pitcher for the Nationals, on average, has a 0.250 probability of hitting the ball in a single \"at bat\". In one game, he gets 6 \"at bats.\"<BR>\n" );
document.write( "(a) Let X be the number of hits that Max gets. As we know, the distribution of X is a binomial probability distribution. What is the number of trials (n), probability of successes (p) and probability of failures (q), respectively?<BR>\n" );
document.write( "(b) Find the probability that he gets at least 4 hits in the one game. (Round the answer to 3 decimal places) Show all work. Just the answer, without supporting work, will receive no credit.<BR>\n" );
document.write( "11. Assume that gas mileage for cars is normally distributed with a mean of 23.5 miles per gallon and a standard deviation of 10 miles per gallon. Show all work. Just the answer, without supporting work, will receive no credit.<BR>\n" );
document.write( "(a) What is the probability that a randomly selected car gets between 20 and 25 miles per gallon? (Round the answer to 4 decimal places)<BR>\n" );
document.write( "(b) Find the 80th percentile of the miles per gallon distribution. (Round the answer to 2 decimal places) </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #736195 by </B><A HREF=/tutors/aboutme.mpl?userid=Boreal><B>Boreal(15235)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=Boreal><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/cgi-bin/show-face.mpl?user=Boreal><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=736195\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> a.  6 trials or n. p=0.250 q=0.750<BR>\n" );
document.write( "b.  4 hits is 6C4 or 15 ways that can happen*0.25^4*0.75^2,=0.0330.<BR>\n" );
document.write( "5 hits is 6*0.25^5*0.75 or 0.0044<BR>\n" );
document.write( "6 hits is 0.25^6 or 0.0002<BR>\n" );
document.write( "At least 4 hits is that sum or 0.0376 or round to 0.038\r<BR>\n" );
document.write( "\n" );
document.write( "Want the z score for this where z=(x-mean)/sd<BR>\n" );
document.write( "z is between (20-23.5)/10 or -0.35 and +0.15<BR>\n" );
document.write( "That probability is 0.1964<BR>\n" );
document.write( "z(0.80)=+0.842<BR>\n" );
document.write( "0.842=(x-mean)/sd<BR>\n" );
document.write( "8.42=x-mean<BR>\n" );
document.write( "x=31.92 mpg </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );