According to the South Dakota Department of Health, the number of hours of TV vi

Question

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 34 hours per week watching TV, and men, 28 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 5.1 hours for the men.

What percent of the women watch TV less than 36 hours per week? (Round your z-score computation and final answer to 2 decimal places.)

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

How many hours of TV do the one 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.)

Explanation / Answer

a) P(X < 36)

= P(z < (36 - 34)/4.8)

= P(z < 0.42)

= 0.6628

= 66.28%

b) P(X > 25)

= P(z > (25 - 28)/5.1)

= P(z > -0.59)

= 0.7224

= 72.24%

c) z score corresponding to top 1% area = 2.33

Hence,

Number of hours top 1 percent of women watch TV = 34 + 2.33*4.8 = 45.184 hours

Number of hours top 1 percent of women watch TV = 28 + 2.33*5.1 = 39.883 hours

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