Question

1. The number of hours spent sleeping each day by teens is normally distributed with a mean of 9 hours and a standard deviation of 1.8 hours

a) Find the probability one teen will sleep over 10 hours in day?

b) If I take a sample of 100 teens, how many of those 100 teens on average will sleep over 10 hours in day?

Answer 1

Part a)

X ~ N ( µ = 9 , σ = 1.8 )
P ( X > 10 ) = 1 - P ( X < 10 )
Standardizing the value
Z = ( X - µ ) / σ
Z = ( 10 - 9 ) / 1.8
Z = 0.5556
P ( ( X - µ ) / σ ) > ( 10 - 9 ) / 1.8 )
P ( Z > 0.5556 )
P ( X > 10 ) = 1 - P ( Z < 0.5556 )
P ( X > 10 ) = 1 - 0.7108
P ( X > 10 ) = 0.2892

Part b)

100 * 0.2892 = 29 teens