0.8944 p is an essential physiological component of health and well being in bot

Question

0.8944 p is an essential physiological component of health and well being in both children and adult.. Am ong infants, short sleep duration and poor sleep quality have been associated with later obesity and deviation of 2 hours Th decimal places.) ehavioral problems." On average, infants six months of age sleep 12.2 hours per day with a standard e recommended sleep range for infants is 10.5 to 18 hours per day. (Round all answers to two a. What is the z-score for an infant getting 10.5 hours of sleep per day? b. What is the z-score for an infant getting 18 hours of sleep per day? c. what percentage of infants get fewer than 10.5 hours of sleep per day? d. What percentage of infants get more than 10.5 hours of sleep per day? e. W -- f. What percentage of infants get the recommended amount of sleep, between 10.5 and 18 hours g. What percentage of infants do not get the recommended amount of sleep, less than 10.5 or h. How much sleep must an infant get to be in the bottom 4th percentile of sleep duration? i. How much sleep must an infant get to be in the top 10th percentile of sleep durations? hat percentage of infants get more than 18 hours of sleep per day? of sleep per day? greater than 18 hours of sep per day? 800t 8.7 hours per The average amount of sleep for an adult is 7.6 hours with a standard deviation of 1.2.With respect to each cohort's distribution of sleep, who is in the highest percentile of sleep: an infant who sleeps 13 hours per day or an adult who sleeps 8 hours per day? -- 0.

Explanation / Answer

Ans:

mean=12.2

standard deviation=2

a)

z(10.5)=(10.5-12.2)/2=-0.85

b)

z(18)=(18-12.2)/2=2.9

c)

(x<10.5)=P(z<-0.85)=0.1977

19.77%

d)

P(x>10.5)=P(z>-0.85)=1-0.1977=0.8023

80.23%

e)

P(x>18)=P(z>2.9)=0.0019

0.19%

f)

P(10.5<x<18)=P(-0.85<z<2.9)=P(z<2.9)-P(z<-0.85)=0.9981-0.1977=0.8005

80.05%

g)P(x<10.5 or x>18)=P(x<10.5)+P(x>18)=P(z<-0.85)+P(z>2.9)=0.1977+0.0019=0.1995

19.95%

h)P(Z<=z)=0.04

z=-1.75

x=12.2-1.75*2=8.7

i)P(Z>=z)=0.1

P(Z<<=z)=1-0.1=0.9

z=1.282

x=12.2+1.282*2=14.76

2)

z(13)=(13-7.6)/1.2=4.5

z(8)=(8-7.6)/1.2=0.33

z(13) is more far away from the mean,so percentile will be more for who sleep 13 hrs.

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