A journal published a study of the lifestyles of visually impaired students. Usi

Question

A journal published a study of the lifestyles of visually impaired students. Using diaries, the students kept track of severalvariables, including number of hours of sleep obtained in a typical day. These visually impaired students had a mean of 8.97 hours and a standard deviation of 2.13 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).

b) Find P(8<x<10

c) Find the value a for which P(x<a)=0.3

Explanation / Answer

a) P(X>12) =1-P(X<12)=1-P(Z<(12-8.97)/2.13)=1-P(Z<1.4225)=1-0.9226 =0.0774

b)P(8<X<10)=P((8-8.97)/2.13<Z<(10-8.97)/2.13)=P(-0.4554<Z<0.4836)=0.6857-0.3245 =0.3612

c)

P(X<a) =0.3

for 30th percentile ; z =-0.5244

hence a =mean +z*Std deviation =8.97-0.5244*2.13=7.853

please revert for any clarification required.

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