http://wiki.stat.ucla.edu/socr/index.php?title=SOCR_Courses_2010_2011_Stat13_1_Lab4&feed=atom&action=historySOCR Courses 2010 2011 Stat13 1 Lab4 - Revision history2024-03-28T14:56:03ZRevision history for this page on the wikiMediaWiki 1.15.1http://wiki.stat.ucla.edu/socr/index.php?title=SOCR_Courses_2010_2011_Stat13_1_Lab4&diff=10645&oldid=prevIvoDinov: Created page with '== Stats 13.1 - Laboratory Activity 4== === Normal Probability Distribution Activity === Note: If at the end of this lab you feel like you…'2010-11-09T22:06:03Z<p>Created page with '== <a href="/socr/index.php/SOCR_Courses_2010_2011_Stat13_1" title="SOCR Courses 2010 2011 Stat13 1"> Stats 13.1</a> - Laboratory Activity 4== === Normal Probability Distribution Activity === Note: If at the end of this lab you feel like you…'</p>
<p><b>New page</b></p><div>== [[SOCR_Courses_2010_2011_Stat13_1 | Stats 13.1]] - Laboratory Activity 4==<br />
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=== Normal Probability Distribution Activity ===<br />
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Note: If at the end of this lab you feel like you could use some more examples, see: [[SOCR EduMaterials Activities Normal Probability examples]]<br />
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'''Description''': You can access the [http://www.socr.ucla.edu/htmls/SOCR_Distributions.html SOCR distribution applets here]. <br />
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====Exercise 1==== <br />
Use SOCR to graph and print the distribution of <math> X \sim N(20, 3) </math>. Show on the graph the following points: <math>\mu \pm 1 \sigma, \mu \pm 2 \sigma, \mu \pm 3 \sigma </math>. How many standard deviations from the mean is the value <math> x=27.5 </math>?<br />
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====Exercise 2==== <br />
Graph the distribution of <math> X \sim N(40, 10)</math>. <br />
# Find <math>P(X>49) </math> Submit a printout.<br />
# Find <math>P(X<22) </math> Submit a printout.<br />
# Find <math>P(12<X<37) </math> Submit a printout.<br />
# Use the mouse or the left cut off or right cut off points to find the <math>8^{th}, 20^{th}, 45^{th}, 55^{th}, 70^{th}, 95^{th} </math> percentiles. After you find these percentiles submit a printout for each one of them.<br />
# Make sure you know how to answer the above questions using the <math>z</math> score <math>z=\frac{x-\mu}{\sigma}</math> and your <math>z</math> table from the handout! You do not need to submit anything here.<br />
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====Exercise 3==== <br />
The lifetime of tires of brand <math>A</math> follows the normal distribution with mean 40000 miles and standard deviation 4000 miles. <br />
# Use <math>SOCR</math> to find the probability that a tire will last between 40000 and 46000 miles.<br />
# Given that a tire will last more than 46000 miles what is the probability that it will last more than 50000 miles? Submit a printout and explain how you get the answer.<br />
# Given that a tire will last more than 46000 miles what is the probability that it will last less than 50000 miles? Submit a printout and explain how you get the answer.<br />
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====Exercise 4====<br />
# The probability that a student is admitted in the Math Department Major at a college is <math>45 \%</math>. Suppose that this year 100 students will apply for admission into the Math major. <br />
# What is the distribution of the number of students admitted? Use <math>SOCR</math> to graph and print this distribution. What is the shape of this distribution? What is the mean and standard deviation of this distribution?<br />
# Write an expression for the exact probability that among the 100 students at least 55 will be admitted.<br />
# Use SOCR to compute the probability of part (3).<br />
# Use the normal distribution applet in SOCR to approximate the probability of part (3) (do not forget the continuity correction). What is the error of the approximation?<br />
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Below you can see the distribution of a normal random variable <math> X </math> with <math> \mu=50, \sigma=5 </math>. In this graph you can also see the probability that <math> X </math> is between 53 and 60.<br />
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<center>[[Image: SOCR_Activities_Christou_normal.jpg|600px]]</center><br />
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* SOCR Home page: http://www.socr.ucla.edu<br />
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