13. The amount of sleep foe American men follows hours and standard devi 3 hours

Question

13. The amount of sleep foe American men follows hours and standard devi 3 hours, I take a sua mormal diseribution wits mean 69 s hours. 1 take SRS of S en (assume that their sleep amounts are independent) ation 1.5 a. Find the probability that a randomly e points) hosen man gets more than & hours of sieep. 3 b. Find the probability that none of the 5 men get more than 8 hours of sleep. (3 points) c. Find the probability that at least one of the 5 men gets more than 8 hours of sleep. (6 points)

Explanation / Answer

Ans:

Given that

mean=6.9

standard deviation=1.5

a)

z(8)=(8-6.9)/1.5=0.73

P(z>0.73)=1-P(z<0.73)=1-0.768=0.232

b)Let x be the number of persons who sleep more than 8 hrs.

Then,x has Binomial distribution with n=5,p=0.232

P(none)=P(x=0)=5C0*0.2320*0.7685=0.267

c)P(atleast one)=P(x>=1)=1-P(x=0)=1-0.267=0.733

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