Question

Using diaries for many weeks, a study on the lifestyles of visually impaired students was conducted. The students kept track of many lifestyle variables including how many hours of sleep obtained on a typical day. Researchers found that visually impaired students averaged 9.22 hours of sleep, with a standard deviation of 1.01 hours. Assume that the number of hours of sleep for these visually impaired students is normally distributed. (a) What is the probability that a visually impaired student gets at most 6.4 hours of sleep? Express your answer as a percent rounded to 2 decimal places. e.g. 1.23% Do not include the % symbol in your answer. Answer: (b) What is the probability that a visually impaired student gets between 7.4 and 7.99 hours of sleep? Express your answer as a percent rounded to 2 decimal places. e.g. 1.23% Do not include the % symbol in your answer. Answer: (C) What is the probability that a visually impaired student gets at least 8.1 hours of sleep? Express your answer as a percent rounded to 2 decimal places. e.g. 1.23% Do not include the % symbol in your answer. Answer: (d) What is the sleep time that cuts off the top 30.3% of sleep hours? Round your answer to 2 decimal places. Answer: hours (e) If 600 visually impaired students were studied, how many students would you expect to have sleep times of more than 7.99 hours? Round to the nearest whole number. Answer: students

Answer 1

Fore given date distribution Normee H-१,२२ 6 = 1. 01 @ PC 6.4) _ 229c-4 222-4 6.५-१.२२ 1.01 = २.११ P (05 6.4) P(2 < - २.१२१) -000262 -0.31, 0 P(न.4 २४८ २.११) 47.4 22 - 7.११-१.२२ 7 - 7,4- १.२२ ION - - ). 6०२० ..) 22 = -1,2178 .. P (7.4 27-११) P (-1.60२० ₹2'-).२) २४) =P(22-1.२)न) -P ( 22-).४०२०) = 0.10 165 -0.03578 = 0.07587 क.597. CScanned with CamScanner

Date Page =) at least 8. I hours of sleep. 2 8.1-9.22 1.01 =-1.1089 Pla7801) = P127 -1.1089) = I-Plze-1.1089) = 1-0.13374 = 0.8663 ~186.63'. @ cut off for to p 30.3. - cehich means, ploc72) = 0,303 Z= 0.516 2 =0c-4 0.576= -9.22 1.ol p= 9.74 CSScanned with CamScanner

Data Page 11 @ n=600 Sleep time more than 7.99 hours. PC0C77.99) 2.7.99-9.82 lool =-1.7178 P (077.99) =P(27+1.2178) a I-P(ZZ-1.8176) = 1- 0.11165 = 0.88835 =188.84 ... | - Number of students = Goox0.88835 =5331 h First quartile p00022) = 0,25 niz = -0.674 2= 26-4 ot -0.674= O(- 9.92 100) Loc=8.54 hours scanned-with-Canscanner