onnect Homework Question 6 (of 6) ahe: 3.00 points According to the South Dakota
ID: 3063479 • Letter: O
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onnect Homework Question 6 (of 6) ahe: 3.00 points 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. a. 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.) Probability b. 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.) Probability c. 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.) Number of hours Women Men ReterencesBook& ResourcesExplanation / Answer
a)The average time women spent on watching TV is 36 hours per week.
Standard deviation among the women is 4.8 hours
Therefore, the percent of women that watch TV less than 38 hours per week is:
Z-score=(38-36)/4.8=2/4.8=0.42 (rounded to two decimal places)
P(Z<0.42)=Area under the standard normal curve to the left of Z=0.42
P(Z<0.42)=0.6591 or 65.91%
Therefore 65.91% of the women watch TV less than 38 hours per week.
b)The average time men spent on watching TV is 30 hours per week.
Standard deviation among the women is 5.2 hours
Therefore, the percent of men that watch TV more than 25 hours per week is:
Z-score=(25-30)/5.2=-5/5.2=-0.96 (rounded to two decimal places)
P(Z>-0.96)=Area under the standard normal curve to the right of Z=-0.96
P(Z>-0.96)=0.8315 or 83.15%
Therefore 83.15% of the men watch TV more than 25 hours per week.
c)The z-score that separates the top 3% is 1.88 (rounded to two decimal places).
Women:
4.8*1.88+36=45.024 hours
A woman who watches more than 45.024 hours of TV per week is in the top 3%.
Men:
5.2*1.88+30=39.776 hours
A man who watches more than 39.776 hours of TV per week is in the top 3%.
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