document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1058353>Question 1058353</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Question<BR>\n" );
document.write( "A company claims that 80% of its trainees are promoted within the first year. Find the probabilities among 8 randomly selected trainees. <BR>\n" );
document.write( "1. At least 6 will be promoted.<BR>\n" );
document.write( "2. From 5 to 7 will be promoted<BR>\n" );
document.write( "3. At most 6 will be promoted.<BR>\n" );
document.write( "4. None will be promoted<BR>\n" );
document.write( "Question<BR>\n" );
document.write( "During rush periods, accidents happen in Nicosia at a rate of 2 per hour. The morning rush period lasts for 1 hour 30 minutes, and the evening rush period for two hours.<BR>\n" );
document.write( "1. What is the probability that there will be no accidents during the morning rush period?<BR>\n" );
document.write( "2. What is the probability of 2 accidents during the evening?<BR>\n" );
document.write( "3. What is the probability of four or more accidents during the morning?<BR>\n" );
document.write( "4. What is the probability that there will be no accidents during both the morning and evening rush period?<BR>\n" );
document.write( "Question<BR>\n" );
document.write( "We have the following data:<BR>\n" );
document.write( "y	x<BR>\n" );
document.write( "6.2	12.3<BR>\n" );
document.write( "8	13.7<BR>\n" );
document.write( "8.4	14.5<BR>\n" );
document.write( "5.3	11.2<BR>\n" );
document.write( "7.2	13.2<BR>\n" );
document.write( "8.7	14.1<BR>\n" );
document.write( "5.7	12\r<BR>\n" );
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document.write( "Calculate the following:<BR>\n" );
document.write( "1.	Means<BR>\n" );
document.write( "2.	Variances and Standard deviations<BR>\n" );
document.write( "3.	Correlation coefficient<BR>\n" );
document.write( "4.	Find the regression(least square)estimator<BR>\n" );
document.write( "5.	Use the regression to predict Y when x=5\r<BR>\n" );
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document.write( "Question	<BR>\n" );
document.write( "A.	We have collected data for the absences of 50 students with days of the week:<BR>\n" );
document.write( " 	Monday	Tuesday	Wednesday	Thursday	Friday<BR>\n" );
document.write( "Absences	14	7	4	9	16<BR>\n" );
document.write( "Test if the absences are equally distributed over all days of the week (critical value=6.251).<BR>\n" );
document.write( "B.	The following table shows the effect on three types of inhalers that helps people breathing who suffer from asthma.<BR>\n" );
document.write( " 	Type of inhaler<BR>\n" );
document.write( "Result	A	B	D<BR>\n" );
document.write( "Recovery	25	15	21<BR>\n" );
document.write( "No effect	36	10	13<BR>\n" );
document.write( "Test whether there is no association between the type of inhaler and the effect (value=7.815).\r<BR>\n" );
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document.write( "Question<BR>\n" );
document.write( "It has been found that the times taken by people to complete the income tax form follows a Normal distribution with a mean of 100 minutes and a standard deviation of 20 minutes.<BR>\n" );
document.write( "Calculate the following probabilities:<BR>\n" );
document.write( "1.	A person takes 110 minutes or more to complete the form<BR>\n" );
document.write( "2.	A person takes between 100 and 125 minutes to complete the form<BR>\n" );
document.write( "3.	A person takes between 75 and 115 minutes to complete the form<BR>\n" );
document.write( "4.	A person takes less than 120 minutes to complete the form\r<BR>\n" );
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document.write( "Question<BR>\n" );
document.write( "A company claims that 80% of its trainees are promoted within the first year. Find the probabilities among 8 randomly selected trainees. <BR>\n" );
document.write( "1. At least 6 will be promoted.<BR>\n" );
document.write( "2. From 5 to 7 will be promoted<BR>\n" );
document.write( "3. At most 6 will be promoted.<BR>\n" );
document.write( "4. None will be promoted<BR>\n" );
document.write( "Question<BR>\n" );
document.write( "During rush periods, accidents happen in Nicosia at a rate of 2 per hour. The morning rush period lasts for 1 hour 30 minutes, and the evening rush period for two hours.<BR>\n" );
document.write( "1. What is the probability that there will be no accidents during the morning rush period?<BR>\n" );
document.write( "2. What is the probability of 2 accidents during the evening?<BR>\n" );
document.write( "3. What is the probability of four or more accidents during the morning?<BR>\n" );
document.write( "4. What is the probability that there will be no accidents during both the morning and evening rush period?<BR>\n" );
document.write( "Question<BR>\n" );
document.write( "We have the following data:<BR>\n" );
document.write( "y	x<BR>\n" );
document.write( "6.2	12.3<BR>\n" );
document.write( "8	13.7<BR>\n" );
document.write( "8.4	14.5<BR>\n" );
document.write( "5.3	11.2<BR>\n" );
document.write( "7.2	13.2<BR>\n" );
document.write( "8.7	14.1<BR>\n" );
document.write( "5.7	12\r<BR>\n" );
document.write( "\n" );
document.write( "Calculate the following:<BR>\n" );
document.write( "1.	Means<BR>\n" );
document.write( "2.	Variances and Standard deviations<BR>\n" );
document.write( "3.	Correlation coefficient<BR>\n" );
document.write( "4.	Find the regression(least square)estimator<BR>\n" );
document.write( "5.	Use the regression to predict Y when x=5\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "Question	<BR>\n" );
document.write( "A.	We have collected data for the absences of 50 students with days of the week:<BR>\n" );
document.write( " 	Monday	Tuesday	Wednesday	Thursday	Friday<BR>\n" );
document.write( "Absences	14	7	4	9	16<BR>\n" );
document.write( "Test if the absences are equally distributed over all days of the week (critical value=6.251).<BR>\n" );
document.write( "B.	The following table shows the effect on three types of inhalers that helps people breathing who suffer from asthma.<BR>\n" );
document.write( " 	Type of inhaler<BR>\n" );
document.write( "Result	A	B	D<BR>\n" );
document.write( "Recovery	25	15	21<BR>\n" );
document.write( "No effect	36	10	13<BR>\n" );
document.write( "Test whether there is no association between the type of inhaler and the effect (value=7.815).\r<BR>\n" );
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document.write( " </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #673433 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=673433\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> 1. 8C6(.8^6)(.2^2)=0.2936<BR>\n" );
document.write( "8C7(.8^7)(.2)=0.3355<BR>\n" );
document.write( "8C8(.8^8)=0.1678<BR>\n" );
document.write( "Sum is 0.7969.<BR>\n" );
document.write( "2. 8C5(.8^5)(.2)^3=0.1468<BR>\n" );
document.write( "Add in the above two for 6 and 7 and the total is 0.7759<BR>\n" );
document.write( "3.At most 6 means everything but 7 and 8, whose collective sum is 0.5033. The probability is the complement or 0.4967.<BR>\n" );
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document.write( "Poisson distribution and parameter is proportional to time<BR>\n" );
document.write( "Morning rush hour would have a parameter equal to 2*1.5 or 3<BR>\n" );
document.write( "probability of no accidents is e^(-3)*3^0/0!=e^(-3)=0.0498.<BR>\n" );
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document.write( "Here the parameter is 2*2 or 4. and we want x=2.  It is e^(-4)*4^2/2=0.1465.<BR>\n" );
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document.write( "Find probability of 0,1,2,3 accidents in the morning.<BR>\n" );
document.write( "for 0 it is 0.0498<BR>\n" );
document.write( "for 1 it is 3 times that or 0.1494<BR>\n" );
document.write( "for 2 it is e^(-3)*3^2/2=0.2240<BR>\n" );
document.write( "for 3 it is e^(-3)*27/6=0.2240.<BR>\n" );
document.write( "total is 0.6473, so complement and answer is 0.3527.<BR>\n" );
document.write( "----------------------------<BR>\n" );
document.write( "Morning probability is 0.0498. Evening is 0.0183.  Joint probability is 0.0009\r<BR>\n" );
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