A journal published a study of the lifestyles of visually impaired students. Using​ diaries, the students kept track of several​ variables, including number of hours of sleep obtained in a typical day. These visually impaired students had a mean of 9.71 hours and a standard deviation of 2.06 hours. Assume that the distribution of the number of hours of sleep for this group of students is approximately normal. Complete parts a through c. a. Find ​P(x>​12).

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A journal published a study of the lifestyles of visually impaired students. Using​ diaries, the students kept track of several​ variables, including number of hours of sleep obtained in a typical day. These visually impaired students had a mean of
9.71
hours and a standard deviation of
2.06
hours. Assume that the distribution of the number of hours of sleep for this group of students is approximately normal. Complete parts a through c.
a. Find
​P(x>​12).
 
​P(x>​12)=0.13310.1331
​(Round to four decimal places as​ needed.)
b. Find
​P(8<x<​10).
 
​P(8<x<​10)=0.35270.3527
​(Round to four decimal places as​ needed.)
c. Find the value a for which
​P(x<​a)=0.3.
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