According to the South Dakota Department of Health the numbe

According to the South Dakota Department of Health, the number of hours of TV viewing per week is higher among adult women than adult men. A recent study showed women spent an average of 36 hours per week watching TV, and men, 30 hours per week. Assume that the distribution of hours watched follows the normal distribution for both groups, and that the standard deviation among the women is 4.8 hours and is 5.2 hours for the men.

What percent of the women watch TV less than 38 hours per week? (Round z-score computation to 2 decimal places and your final answer to 4 decimal places.)

What percent of the men watch TV more than 25 hours per week? (Round z-score computation to 2 decimal places and your final answer to 4 decimal places.)

How many hours of TV do the three percent of women who watch the most TV per week watch? Find the comparable value for the men. (Round your answers to 3 decimal places.)

Solution

a)
Mean ( u ) =40
Standard Deviation ( sd )=4.7
Normal Distribution = Z= X- u / sd ~ N(0,1)                  

P(X < 43) = (43-40)/4.7
= 3/4.7= 0.6383
= P ( Z <0.6383) From Standard Normal Table
= 0.7384                  
b)
Mean ( u ) =34
Standard Deviation ( sd )=5.2
Normal Distribution = Z= X- u / sd ~ N(0,1)                  

P(X > 30) = (30-34)/5.2
= -4/5.2 = -0.7692
= P ( Z >-0.769) From Standard Normal Table
= 0.7791                  
c)
FOR WOMEN
P ( Z < x ) = 0.03
Value of z to the cumulative probability of 0.03 from normal table is -1.881
P( x-u/s.d < x - 40/4.7 ) = 0.03
That is, ( x - 40/4.7 ) = -1.88
--> x = -1.88 * 4.7 + 40 = 31.1593                  

FOR MEN
P ( Z < x ) = 0.03
Value of z to the cumulative probability of 0.03 from normal table is -1.881
P( x-u/s.d < x - 34/5.2 ) = 0.03
That is, ( x - 34/5.2 ) = -1.88
--> x = -1.88 * 5.2 + 34 = 24.2188