Newborn Babies & Tuition Rates 1) According to kidshealth.org, newborn babies typically sleep between 14-17 hours in a 24-hour period. Let's assume that sleep times are normally distributed with a mean of 15.5 hours and a standard deviation of 0.5 hours. Use the empirical rule to answer the following questions. Draw and shade a normal distribution to support your answer. a) What percent of babies get between 15.5 hours and 16 hours of sleep? b) What percent of babies get between 14.5 hours and 16 hours of sleep? c) What percent of babies get more than 16 hours of sleep? d) How many hours of sleep would a baby need to get to be in the top 2.5% of sleep times? e) What percentage of babies get between 15 and 16.25 hours of sleep? You may wish to convert to z-scores and use this Desmos calculator page to determine the percentage. https://www.desmos.com/calculator/5ubvhyrip7 2) Super heavy pumpkins are showcased each year at the state fair. These pumpkins have weights that are normally distributed with a mean weight of 15.1 kilograms and a standard deviation of 2.2 kilograms. What is the approximate percent of all super heavy pumpkins that weigh between 13.0 kilograms and 16.5 kilograms? Explain using the empirical rule why an answer of 75% is not reasonable. 3) How are tuition rates distributed among private colleges in Pennsylvania? The data here (Tuition) was obtained from https://www.collegetuitioncompare.com. Schools that did not list acceptance rates (which were primarily technical and trade schools) were removed from the data set. a) Calculate the mean and standard deviation for the data set. NOTE: This can be done by typing the commands average(C2:C113) and stdev(C2:C113) in a cell of the spreadsheet. b) If the distribution of tuition was approximately normal, what would be the range for the middle 68% of tuition rates? c) If the distribution of tuition was approximately normal, what would be the range for the middle 95% of tuition rates? d) If the distribution of tuition was approximately normal, what would be the range for the middle 99.7% of tuition rates? e) What percent of the distribution is within 1 standard deviation? f) What percent of the distribution is within 2 standard deviations? g) What percent of the distribution is within 3 standard deviations? h) Based on your results to the previous questions, do you think tuition at private colleges in Pennsylvania are normally distributed? Explain. i) Go to the Desmos Calculator page at www.desmos.com/calculator/zmuhx8wgnj and click on the circles in front of lines 3 & 4. Explain how the histogram of the distribution and the normal distribution shown support your answer to the previous question. Undergraduate Acceptance Graduation Student To Student School Name City Curtis Institute of Music Philadelphia Tuition & Fees Rate Rate faculty Population 2525 0.04 0.69 2 to 1 171 Western Pennsylvania Hos Pittsburgh 9580 0.72 0.5 11 to 1 123 Talmudical Yeshiva of Phila Philadelphia 9725 0.75 0.62 19 to 1 123 Yeshivath Beth Moshe Scranton 9800 0.86 0.71 6 to 1 33 Laurel Business Institute Uniontown 10912 0.91 0.8 10 to 1 232 Laurel Technical Institute Sharon 10912 0.92 0.76 9 to 1 168 Laurel Technical Institute MEADVILLE 10912 0.92 0.5 8 to 1 115 Bidwell Training Center Inc Pittsburgh 12000 0.89 0.69 10 to 1 115 The Workforce Institute's (Philadelphia 12097 0.5 1 7 to 1 8 Reading Hospital School of Reading 12899 0.23 0.57 8 to 1 329 UPMC Jameson School of New Castle Studio Incamminati 13051 1 6 to 1 56 Philadelphia 13885 0.76 5 to 1 40 Pittsburgh Career Institute Pittsburgh 15064 0.9 0.42 9 to 1 136 Rosedale Technical College Pittsburgh 15125 0.6 0.79 15 to 1 417 Orleans Technical College Philadelphia 15273 0.61 0.74 20 to 1 284 UPMC Shadyside School of Pittsburgh 15545 0.44 4 to 1 263 UPMC St. Margaret School Pittsburgh 15545 0.64 0.5 14 to 1 102 UPMC Mercy School of Nu Pittsburgh 15545 0.67 0.52 14 to 1 173 DeVry University-Pennsylv: Ft. Washington 15648 0.9 0.16 25 to 1 297 Keystone College La Plume 17000 0.79 0.47 12 to 1 1,424 Penn Commercial Business Washington 17313 0.75 0.51 14 to 1 237 South Hills School of Busin State College 18475 0.96 0.61 7 to 1 406 Manor College Jenkintown 18530 0.86 0.32 12 to 1 747 Geisinger-Lewistown Hosp Lewistown 18710 0.51 0.71 10 to 1 51 92-23 Central Penn College Summerdale 18714 0.84 0.4 9 to 1 1,047 Grove City College Grove City 18930 0.79 0.85 13 to 1 2,338 Johnson College Scranton 20025 0.97 0.56 9 to 1 428 Ohio Valley Hospital Schoo McKees Rocks 20275 0.8 11 to 1 80 Rosemont College Rosemont 20650 0.92 0.49 11 to 1 945 New Castle School of Trade New Castle 20736 1 0.71 11 to 1 454 Hussian College-Philadelph Philadelphia York College of Pennsylvan York 21428 1 0.7 8 to 1 81 21700 0.69 0.63 14 to 1 4,317 Saint Charles Borromeo Se Wynnewood 22570 0.4 7 to 1 227 University of Valley Forge Phoenixville 22606 0.63 0.45 10 to 1 659 The Restaurant School at V Philadelphia 23550 0.98 0.67 21 to 1 335 Mount Aloysius College Cresson 24370 0.95 0.48 11 to 1 1,784 Bryn Athyn College of the Bryn Athyn 25449 0.92 0.58 6 to 1 305 Pittsburgh Institute of Mor Pittsburgh 25610 0.63 0.92 17 to 1 217 Clarks Summit University South Abington T 26082 0.41 0.88 11 to 1 768 Wilson College Chambersburg 26090 0.93 0.64 12 to 1 1,499 Waynesburg University Waynesburg 26500 0.93 0.66 13 to 1 1,674 Albright College Reading 26688 0.85 0.57 15 to 1 1,934 Lancaster Bible College Lancaster 27010 0.96 0.62 14 to 1 2,122 Pennsylvania College of Ar Lancaster 27650 0.43 0.44 10 to 1 251 Immaculata University Immaculata 27750 0.81 0.67 9 to 1 2,448 Williamson College of the Media 28320 0.32 0.73 10 to 1 257 University of the Sciences Philadelphia 28683 0.71 0.78 7 to 1 2,231 Geneva College Beaver Falls 29040 0.53 0.72 12 to 1 1,543 DLP Conemaugh Memoria Johnstown 29350 0.8 0.89 10 to 1 212 Cairn University-Langhorn Langhorne Pennsylvania College of He Lancaster 29553 0.83 0.6 11 to 1 1,143 29922 0.78 0.63 12 to 1 1,800 La Roche University Pittsburgh 30320 0.99 0.55 12 to 1 1,443 Carlow University Pittsburgh 31446 0.92 0.57 12 to 1 2,076 Holy Family University Philadelphia 31640 0.73 0.58 12 to 1 3,089 Robert Morris University Moon Township 32130 0.84 0.65 15 to 1 4,895 La Salle University Philadelphia 32425 0.78 0.66 12 to 1 5,191 Neumann University Aston 32960 0.62 0.52 14 to 1 2,598 Elizabethtown College Elizabethtown 32960 0.81 0.69 11 to 1 1,687 Thiel College Greenville 33520 0.79 0.53 11 to 1 742 Cabrini University Radnor 33845 0.76 0.55 13 to 1 2,285 Point Park University Pittsburgh 34200 0.73 0.6 12 to 1 4,099 Eastern University Saint Davids 34706 0.61 0.59 10 to 1 3,256 Gannon University Erie 35541 0.76 0.68 13 to 1 4,291 Misericordia University Dallas 35940 0.86 0.68 11 to 1 2,566 Citizens School of Nursing Tarentum 36134 0.8 10 to 1 165 Gwynedd Mercy University Gwynedd Valley 36807 0.95 0.6 10 to 1 3,056 Marywood University Scranton 36928 0.78 0.68 12 to 1 2,853 Messiah University Mechanicsburg 37180 0.76 0.79 12 to 1 3,375 Saint Vincent College Latrobe 37604 0.68 0.69 11 to 1 1,867 Westminster College New Wilmington 37675 0.67 0.7 11 to 1 1,269 Seton Hill University Greensburg 37946 0.76 0.65 14 to 1 2,297 Alvernia University Reading 38030 0.64 0.63 12 to 1 2,792 Chestnut Hill College Philadelphia 38200 0.65 0.56 10 to 1 1,794 Wilkes University Wilkes-Barre 38752 0.79 0.63 12 to 1 5,132 DeSales University Center Valley 39500 0.79 0.69 14 to 1 3,438 Chatham University Pittsburgh 39902 0.62 0.7 10 to 1 2,336 Saint Francis University Loretto 39928 0.75 0.73 14 to 1 2,611 King's College Wilkes-Barre 40080 0.81 0.64 13 to 1 2,569 Pennsylvania Academy of 1 Philadelphia 40376 0.88 0.64 7 to 1 273 Delaware Valley University Doylestown 40620 0.93 0.6 13 to 1 2,428 Mercyhurst University Erie 41350 0.86 0.68 14 to 1 2,685 Cedar Crest College Allentown 41567 0.61 0.51 10 to 1 1,596 Thomas Jefferson Universi Philadelphia 41715 0.66 0.7 12 to 1 7,786 Duquesne University Pittsburgh 41892 0.74 0.81 13 to 1 9,274 Lycoming College Williamsport 42714 0.62 0.67 12 to 1 1,142 Moore College of Art and Philadelphia 44806 0.47 0.72 7 to 1 397 Arcadia University Glenside 45320 0.66 0.66 12 to 1 3,662 Lebanon Valley College Annville 46030 0.8 0.78 10 to 1 1,922 The University of the Arts Philadelphia 46680 0.73 0.61 8 to 1 1,914 University of Scranton Scranton 47084 0.76 0.83 13 to 1 5,286 Moravian College Bethlehem 47367 0.75 0.69 11 to 1 2,514 Saint Joseph's University Philadelphia 47940 0.75 0.81 11 to 1 7,589 Widener University Chester 48575 0.72 0.65 13 to 1 6,621 Juniata College Huntingdon 49175 0.71 0.78 11 to 1 1,433 Washington & Jefferson C Washington 50170 0.85 0.75 11 to 1 1,357 Allegheny College Meadville 50980 0.62 0.74 10 to 1 1,771 Susquehanna University Selinsgrove 51140 0.72 0.72 12 to 1 2,396 Bryn Mawr College Bryn Mawr 54440 0.33 0.84 9 to 1 1,690 Swarthmore College Swarthmore 54456 0.09 0.94 8 to 1 1,559 Muhlenberg College Allentown 54600 0.66 0.84 10 to 1 2,340 Lafayette College Easton 54992 0.31 0.88 10 to 1 2,642 Ursinus College Collegeville 55210 0.79 0.81 10 to 1 1,435 Lehigh University Bethlehem 55260 0.32 0.9 9 to 1 6,849 Drexel University Dickinson College Villanova University Philadelphia 56238 0.75 0.69 11 to 1 24,634 Carlisle 56498 0.4 0.83 9 to 1 2,399 Villanova 57460 0.28 0.9 11 to 1 11,030 Bucknell University Lewisburg 58202 0.34 0.9 9 to 1 3,668 Carnegie Mellon University Pittsburgh 58485 0.15 0.9 10 to 1 14,029 Gettysburg College Gettysburg 58500 0.48 0.81 9 to 1 2,441 Haverford College Haverford 58900 0.16 0.9 8 to 1 1,310 University of Pennsylvania Philadelphia 60042 0.08 0.96 6 to 1 25,860 Franklin and Marshall Colle Lancaster 61062 0.3