Question 1112177: The AC Nielsen Company reported in the Nielsen Report on Television that the distribution of weekly television viewing time for children aged 2-11 years is normally distributed with a mean of 24.5 hours and a standard deviation of 6.23 hours.
Draw a complete graph of each situation and find the answer.
a. What percent of children aged 2 – 11 watch more than 30 hours per week?
b. What percent of children aged 2 – 11 watch fewer than 10 hours per week?
c. What percent of children aged 2 – 11 watch between 20 and 25 hours per week?
d. How many hours of TV watching per week defines the children who are in the top 10%?
e. What are the three quartiles for the distribution described above?
Answer by Boreal(15235)   (Show Source):
You can put this solution on YOUR website! Normal curve has mean at 24.5, and -1sd at 18.27, -2sd at 12.04, and -3 sd at 5.81. It has + 1sd at 30.73, +2sd at 36.96 and +3sd at 43.19
a. z=(x-mean)/sd, which is z > (30-24.5)/6.23 or z > 0.88, probability is 0.1887
b. z < (10-24.5)/6.23 or z < -2.33, probability is 0.0100
c. z between -0.72 and +0.08, probability is 0.2961
d. top 10% is z=+1.28 or 7.97 above the mean or greater than 32.47 or 32.5
e. 1 and 3 quartiles are +/- z=0.674 or +/- 4.20
Q1 is 20.3
Q2 is 24.5
Q3 is 28.7
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