Answer to Question #112358 in Statistics and Probability for meem

Question

According to the Sleep Foundation, the average night’s sleep is 7 hours. Assume the standard deviation is 0.5 hours and that the probability distribution is normal.
a. What is the probability that a randomly selected person sleeps more than 9 hours?
b. What is the probability that a randomly selected person sleeps 5 hours or less?
c. What is the probability that a randomly selected person sleeps exactly 10 hours?
d. What is the probability that a randomly selected person sleeps more than 7 hours?
e. Doctors suggest getting between 7 and 9 hours of sleep each night. What percentage of the population gets this much sleep?

Answer 1

a)P(x>9),

z=(x-m)/sd=(9-7)/0.5=4;

using table: P=1- t(z)=0.00003;

b) P(x<=5),

z=(5-7)/0.5=-4;

using table P=t(z)=0.00003 ;

c)P(X=10)=P(Z=((10-7)/0.5))=p(Z=6)=0,

P=0.

d)P(x>7),

z=(7-7)/0.5=0;

using table P=1-t(0)=0.5

e)P(7<x<9),

z1=(7-7)/0.5=0;

z2=(9-7)/0.5=4;

using table P=t(4)-t(0)=0.99997-0.5=0.49997

P=49.997%