STAT 2507A – June 24

STAT 2507A – June 24 - STAT2507AJune24...

Info iconThis preview shows pages 1–7. Sign up to view the full content.

View Full Document Right Arrow Icon
1 STAT 2507A – June 24 Jerry Situ 8.1-8.4 Summer 2009
Background image of page 1

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
Review of CLT by example In the class of 70, the student marks are normally  distributed with a mean of 75 and a standard  deviation of 10. 1) What is the probability that a randomly selected  student has a mark higher than 80%. 2) What is the probability that four randomly selected  students have an average mark higher than 80%. 3) Graph the distribution for #1 and #2. 2
Background image of page 2
Solution 1) Let X be the mark of a randomly selected student. Given: X ~ N(75,10) Want: P(X>80) = P((X-μ)/ σ  > (80-75)/10) =P(Z>.5) = 1-P(Z<.5) = 1 -.6915 = 0.3085 2) let X 1 , X 2 , X 3 , X 4  be the four randomly selected  students. X ~ N(75, 10/√4) by the CLT. ̅ Want: P(X > 80)=P((X – 75)/(10/√4)>(80-75)/(10/√4)  ̅ ̅ =P(Z > 1) = 1 – P(Z<1) = 1 -.8413 = .1587 3
Background image of page 3

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
4 Distribution of X-bar (i.e., what the average  would be if samples of  size 4 were taken over  Distribution of X (i.e., how the marks  are distributed  among the  students)
Background image of page 4
Example 2 The professor will only pass 60% of the  students, in a random sample of 30  students what is the probability that half  of them will pass. 5
Background image of page 5

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
Let X 1 ,…,X 25  be whether or not the randomly selected  students pass. X i  in {0,1} (fail or pass). X i  ~ Bin(1, p)  where p = .6 X ~N(p,sqrt(pq/n)) =N(.6,.089) by the CLT ̅ Want: P(X > .5) = P(Z > (.5-.6)/.089) = P(Z > -1.12) ̅ = P(Z<1.12) = .8686 Note: Also note:  Σ X ~ bin(30,.6). P(X > .5) = P(
Background image of page 6
Image of page 7
This is the end of the preview. Sign up to access the rest of the document.

This note was uploaded on 05/24/2011 for the course STAT 2507 taught by Professor Masoudmollaalizadehnasari during the Summer '09 term at Carleton CA.

Page1 / 19

STAT 2507A &amp;acirc;€“ June 24 - STAT2507AJune24...

This preview shows document pages 1 - 7. Sign up to view the full document.

View Full Document Right Arrow Icon
Ask a homework question - tutors are online