Question

According to the South Dakota Department of Health, the mean number of hours of TV viewing per week is

higher among adult women than men. A recent study showed women spent an average of 34 hours per week

watching TV and men 29 hours per week (

www.state.sd.us/DOH/Nutrition/TV.pdf). Assume that the

distribution of hours watched follows the normal distribution for both groups, and that the standard deviation

among the women is 4.5 hours and is 5.1 hours for the men.

a.What is the probability that a woman watches more than 30 hours of TV per week?

b. What is the probability that a man watches more than 30 hours of TV per week?

Answer 1

Part a)
X ~ N ( µ = 34 , σ = 4.5 )
P ( X > 30 ) = 1 - P ( X < 30 )
Standardizing the value
Z = ( X - µ ) / σ
Z = ( 30 - 34 ) / 4.5
Z = -0.8889
P ( ( X - µ ) / σ ) > ( 30 - 34 ) / 4.5 )
P ( Z > -0.8889 )
P ( X > 30 ) = 1 - P ( Z < -0.8889 )
P ( X > 30 ) = 1 - 0.187
P ( X > 30 ) = 0.8130

Part b)
X ~ N ( µ = 29 , σ = 5.1 )
P ( X > 30 ) = 1 - P ( X < 30 )
Standardizing the value
Z = ( X - µ ) / σ
Z = ( 30 - 29 ) / 5.1
Z = 0.1961
P ( ( X - µ ) / σ ) > ( 30 - 29 ) / 5.1 )
P ( Z > 0.1961 )
P ( X > 30 ) = 1 - P ( Z < 0.1961 )
P ( X > 30 ) = 1 - 0.5777
P ( X > 30 ) = 0.4223