### Create a StudySoup account

#### Be part of our community, it's free to join!

Already have a StudySoup account? Login here

# 2 Class Note for STAT 200 at PSU

### View Full Document

## 27

## 0

## Popular in Course

## Popular in Department

This 9 page Class Notes was uploaded by an elite notetaker on Friday February 6, 2015. The Class Notes belongs to a course at Pennsylvania State University taught by a professor in Fall. Since its upload, it has received 27 views.

## Similar to Course at Penn State

## Popular in Subject

## Reviews for 2 Class Note for STAT 200 at PSU

### What is Karma?

#### Karma is the currency of StudySoup.

#### You can buy or earn more Karma at anytime and redeem it for class notes, study guides, flashcards, and more!

Date Created: 02/06/15

835mg 84 The Normal Curve The 2min mus 12mg mus rmnm Em muubmi rmnm Em mm mm Ham The rmnm cm 15 me Emmar symmeme bell shaped curve that s u En used m appmmmale me mmbuuun ufmasurEmEnts m a pupulauun Example The dsmbuuun urme numba39 ur huurs that cullege Studems sleep Bu 2 week mgm 15 appmmmaled by me nurmal curve dsplayed m me gurebeluw Chamdensucs uf39he made was damned rum data culleded ma 5131151155 class amend State Umversny Model for Hours ofSleep n25 um 15 Dansxty um nus nun 234567891U1112 HuursufSleep Frobablllty Equals Area Underthe curve Thevaual ems m me drawmg urme nm39mal curve abuve 152 mm x5111 Wham dansxty scale 15 usedpmbab1hly equals am undEr me curve Example newnkumznnmmaummo m pmmm w w my asses T The pmpumuh ufcullege Students whu sleep belwem s s and a s huurs Ts The am undEr The henna curve hemem s s and a s huurs an area shuwn Th The fulluwmg gure Shaded Avea Pmpumun bemeen 5 5 arm a 5 U2 Dansxty uT uu 23o567aam1112 Hamsafsleep characteristics onhe Normal curve Sumelmpumnl alums unhe numal curve are 0 Theshapexsasymmemcbellcurveshape o Measuremst relauvely class in The man are murepmbable Than measurements relauvely r hum The mm o The tentaclme uTsmhuuuhTsThemah o The spread unhe hen Ts delammed hy the mhuam demauuh TheTe semauy are sevauT pmhahTmy uTsmhuuuh mudels that have these charadensucs The henna curve Ts by rms mug cumm nly usedmudel wnh These alums Notatlon forthe Populauon Mean and Standard Devuauon The henna curve Ts a muuel fur The uTsuThuuuh ufmasur nmls Th 2 pupulauuh o The symbul u Ts used to represem The pnp lla nn m o The symbul o Ts used in represem LhEpnp lla nn Standard dzv39avjnn Fagez The Standard Normal curve Standardized Scores A muubmlizelixmm alsu ned aware masures huw many smhuam demauunsa Wine Ts hum the man nemuwuumznnmmmmam human T w 40 PM ems l A Tulmula fur mlmlaunga mndardlzed seule ls vazusemsan Xe h z s d 17 Example Suppuse lhal lhe man pulse le lh a pepulalleh ls 75 bats pa mlhule and lhe Standard umaueh ls In 0 Fempulselele uf85the Standardizedsc relsl W1uerman sd 8577S1U1 o Furapulseraleuf7EILhezrscurelsrS w1uermansd7lr75ll ens Standamlzeto solve Normal curve Problems Every numal curve pmhlem En he sulved hy euhvmlhg lhe pmhlemle an equmlehl queslmn abuut Standardized scares Example Suppuse lhanhe ulsmhulleh ufpulsemles lh apupulauun ls desmbed bya helmel curve wnh a man ens hmlspelmlhuleahu a Standard umaueh equal le In The s39andardlzed scare Tum pulse le eras ls z 1 Thepmpemuh enhe pepulallehlhal has apulsemte lesslhah as ls alsu lhe pmpullleh lhal has a zescure less lhah l The Standard Normal curve The mulbmirmrmd nave ls a hulmal curve made fur zrscures lh lhls mudel lhe man ls n and lhe s39andard demath ls l The smhuam helmel curve ls used le sulve evay helmel curve pmblem whelher lhe pmhlem ls abuut helghls le huurs ersleep many utherlmnahle Flndlng Areas Under the Standard Normal curve 0 The lame m1ng 232 unhepaskel shuws lhe mam Lhzleflnfz meme 0 Spreadsheelpmgams llke Excel have eemmahuslhal Bitmalenurmal curve eras vieluukusulznnmmalzmmaalv plwnnn l w 40 PM ems l o Gmphmg calmlalurs llke me T1783alsu have cummands that an beused Solvlng Normal curve Problems We nuW dEmunslmlehquu sulve geneel nurmal euwe pmblems As an example we useme nurmal curve made fur cullege Students huurs er sleep Bu 2 week mgm that we descnhed m The Basics39 sechun o Themanlsu7huurs o The slanderd demahun l5 7 l 7 huurs Howto Flnd the Propomon Less Than a value Tu ndme pmpumun ufa pupulauun wllh a wlue less man a spen edwlue l Calculate a zrscure fur me speci ed wlue 2 Delmnelhearatutheleftufthezrscure Example Abuut what pmpumun er students sleepless man s huurs Bu 2 week mgm ms wlll be me am le me left ers huurs Plupumun Sleeplng Less than 5 Huuls Ale la le M5 ls mmquot lessonquot 5 l l234557aalulll2l3 Huuls elsleep The mllnjnn 1 Calculate me slanderdlzed scare fur s huurs ufsleep The funnulals emulwumznnmmmmmu pmmm l w 40 PM 835mg 1 valueimerzn z 7 5d a 118 FurShuurszSr7177217 2 Use 1112131212 un page 2321 ndthearaluthele ufrl 18 Themswms 21mm 11 12 21mm 12 Abuut 12 ufcullege studems sleep less man s huurs Bu 2 week mgm Nave Ithe pmpumun sleepmg less than 5 huurs1s n 12 Lhepmpumun sleepmg mm vhan Shuurs1s 1711 1211 88 Howto Find the Propomon GreaterThan a value Tu ndme pmpumun Ufa pupulauun wnh a wine Wta thana spen edwlue 1 021mm 2 Home fur me speci ed mlue 2 Dela mme39hearaluthele uflhezrscure 3 Araluthengqt amlu helem Examplz Abuulwhalpmpumun ufstudents sleep mure man 111 huurs ma week mgm Tms15 me am tutherighlufl huurs Pvupumun S122pmg Mme 1m 1m Huuvs Ave 0 1111M m m 15 mmquot mm mquot m 1 2345578 9111111213 Huuvs uvs1eep Th2 mllnjnn n1 mumumznnmmmm 5 m pmmm 1 w 40 PM 835mg 1 1 Calculate Lhezrscure fur 1n huurs Z1ne71731717 2 Fmdmeammmemnurzzna Theanswmsabumnga Usep 232 3 Calculate answa39m Step 2 1 719511 n4abuu14 AbuuH Vaufcullegesludemssleep mnmvhanl huurs permgm Howto Flndthe Propomon m an Interval Tu ndme pmpumun Ufa pupulauun 11131 lls ma mended 1mm 1 Calculates zescure fur ach md urme 1mm 2 Fmd me am pmbablhly 1 me le er ach zescure 3 021mm me mffa39mce belwem me Wm pmbabllmes On a week mgm what percentage 11 smdems s1eep belwem s and 111 hequ Th151s me am between 5 huurs and 111 huurs Pvupumun Hemeen 5 and 1m Huuvs 2345578 9111111213 Huuvs uvs1eep Th2 mllnjnn e We lmed mfmmauun 21mm 5 and 1m huurs urs1eep 1n the prevmus Wm su1uuuns 1 Furl huurszl7 FurShuurSz7118 2 Tu the left ufz e 76 me ara1s 21mm 1 96 vieluukummnmmaummwmvMwnnn1w 40 PM Basics 1 To the left ofz 118 the area is about 012 3 The answer is 096 012 084 About 84 of college students sleep between 5 and 10 hours on a week night How to Find a Percentile The term quotpercentile rankquot refers to the area probability to the left of a value For instance we found that the area to the left of 5 hours of sleep is 01190 This means that o the percentile rank for 5 hours is 01190 about 12 o the 12th percentile is 5 hours To find the value corresponding to a specified percentile rank 1 Determine the zscore that has the given percentile rank 2 Figure out what value has that zscore Example What is the 98th percentile of the distribution of hours of sleep The probability to the left of the answer is 098 H ours of Sleep I The solution 1 Find the zscore for which the area to the left is 098 Look for 098 under ProbltZ in the table on page 232 o The value under Z Score is 205 The 98th percentile is 205 standard deviations above the mean 2 Determine the sleep value that has a zscore of 205 fileDRHOstat200normal2htm 7 of 9 3142000 11949 PM Basics 1 o 205 standard deviations is 205 17 35 hours 0 35 hours above the mean of 7 hours 105 hours The 98th percentile of the sleep distribution is 105 hours A formula to calculate the value that has a known zscore is XZ0u For 2 205 X 205 17 7 35 7 105 hours The Empirical Rule and Outliers The following three statements constitute the empirical rule 1 About 68 of the values in a population described by a normal curve are within one standard deviation of the mean 2 About 95 of the values in a population described by a normal curve are within two standard deviations of the mean 3 About 997 of the values in a population described by a normal curve are within three standard deviations of the mean The empirical rule is also called the 68 95 99 7 rule Example The number of hours that college students sleep on a week night is approximated by a normal curve with a mean of 7 hours and a standard deviation of 17 hours 0 About 68 of college students sleep between 53 and 87 hours on a week night The calculation is 7 i 17 0 About 95 of college students sleep between 36 and 104 hours on a week night The calculation is 7 i 217 0 About 997 of college students sleep between 19 and 121 hours in a week night The calculation is 7 i 317 When is a Value an Outlier There is no universally accepted criterion for declaring a point to be an outlier but most data fileDRHOstat200normal2htm 8 of 9 3142000 11949 PM Basics 1 analysts are suspicious when a data values zscore is not between 3 and 3 The motivation for this guideline is that about 997 of the values in a population described by a normal curve are within three standard deviations of the mean In other words nearly all zscores are between 3 and 3 Example In the Penn State sleep survey one student s response was that he had slept 16 hours the previous day Let s see where 16 hours falls in the normal curve model for sleep zl67 l79l7529 This zscore is outside the range 3 to 3 so we call it an outlier We can also use the table on page 232 to find the probability to the left of z 529 The closest zscore in the table is z 5 The probability to the left of this zscore is 09999997 or in percent terms about 9999997 In other words 16 hours of sleep is around the 9999997th percentile of the distribution Quite an accomplishment fileDRHOstat200normal2htm 9 of 9 3142000 11949 PM

### BOOM! Enjoy Your Free Notes!

We've added these Notes to your profile, click here to view them now.

### You're already Subscribed!

Looks like you've already subscribed to StudySoup, you won't need to purchase another subscription to get this material. To access this material simply click 'View Full Document'

## Why people love StudySoup

#### "I was shooting for a perfect 4.0 GPA this semester. Having StudySoup as a study aid was critical to helping me achieve my goal...and I nailed it!"

#### "I used the money I made selling my notes & study guides to pay for spring break in Olympia, Washington...which was Sweet!"

#### "There's no way I would have passed my Organic Chemistry class this semester without the notes and study guides I got from StudySoup."

#### "It's a great way for students to improve their educational experience and it seemed like a product that everybody wants, so all the people participating are winning."

### Refund Policy

#### STUDYSOUP CANCELLATION POLICY

All subscriptions to StudySoup are paid in full at the time of subscribing. To change your credit card information or to cancel your subscription, go to "Edit Settings". All credit card information will be available there. If you should decide to cancel your subscription, it will continue to be valid until the next payment period, as all payments for the current period were made in advance. For special circumstances, please email support@studysoup.com

#### STUDYSOUP REFUND POLICY

StudySoup has more than 1 million course-specific study resources to help students study smarter. If you’re having trouble finding what you’re looking for, our customer support team can help you find what you need! Feel free to contact them here: support@studysoup.com

Recurring Subscriptions: If you have canceled your recurring subscription on the day of renewal and have not downloaded any documents, you may request a refund by submitting an email to support@studysoup.com

Satisfaction Guarantee: If you’re not satisfied with your subscription, you can contact us for further help. Contact must be made within 3 business days of your subscription purchase and your refund request will be subject for review.

Please Note: Refunds can never be provided more than 30 days after the initial purchase date regardless of your activity on the site.