Question

A study claims that the average hours of sleep on a weeknight was 7 hours with a standard deviation of 1.6 hours.

a) How many hours do you (typically) sleep on a weeknight? How many standard deviations above or below the average are your hours of sleep? (Hint: find your standard score).

b) What percentage of individuals sleep less than you do? Show your calculation,

c) What proportion of individuals sleep at least as much as you do? Show your calculation.

Answer 1

let X is  hours of sleep on a weeknight

E(X)=7 SD(X)=1.6

a)

typically i sleep 6 hours on a weeknight

so

difference =7-6 =1 =0.625*1.6 =0.625SD(X)

So my sleep time is 0.625 SD less than average sleep time.

b)

we have to find P(X<6)

now

so required % is 26.6%

c)

we have to find P(X>6)

now

P(X>6)=1-P(X<6) =1-0.266=0.734