Connect Homework Question 6 (of 6) value: 3.00 points According to the South Dak

Question

Connect Homework Question 6 (of 6) value: 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 39 hours per week watching TV, and men, 33 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 4.7 hours and is 5.3 hours for the men a. What percent of the women watch TV less than 43 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 30 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 two 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 References eBook & Resources Worksheet Difficulty 2 Intermediate esc F1

Explanation / Answer

(a) Here for female Average time watching movie = 39 hours per week

standard deviation = 4.7 hour

for male

average time watching movie = 33 hours per week

standard deviation = 5.3 hours

If x is the number of hours tv watched by a women in a week and y is he number of hours tv watched by a man in a week.

Pr(x < 43) = NORMAL( x< 43 ; 39 ; 4.7)

Z = (43 - 39)/4.7 = 0.8511

Pr(x < 43) = NORMAL( x< 43 ; 39 ; 4.7) = Pr(Z < 0.8511) = 0.8026

(b) Pr(Y > 30 hours) = 1 - NORM (Y < 30 hours ; 33 ; 5.3)

Z = (30 - 33)/5.3 = -0.566

Pr(Y > 30 hours) = 1 - NORM (Y < 30 hours ; 33 ; 5.3) = 1 - Pr(Z < -0.566) = 1 - 0.2857 = 0.7143

(c) Let say women top most 2% value is X0 and for men, it is Y0

Pr(x < X0) = 0.98 and Pr(y < Y0 ) = 0.98

The respective z valueis

Z = 2.05375

so for women,

2.05375 = (X0  - 39)/4.7

X0 = 39 + 4.7 * 2.05375 = 48.653 hours per week

Y0 = 33 + 5.3 * 2.05375 = 43.885 Hours per week

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