cylstart/49616316811dion=chresume submissionid=563349497Quiz: Normal Probability Distributions Word Problems 11 of 2Show all work. Round 2-score to nearest hundredth and mean to nearest whole numberPOSSIBLE POINTS: 10mmThe time spent watching television in a week is normally distributed with a standard deviation of 2 hours. If the top 5% of people spend more than 10hours watching TV a week, what is the mean time spent watching TV a week? (Hint find the 2-score first)B 1 v0 / 10000 Word Limit<2Next

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Answer

Mean time spent watching TV a week = 6.71 hours

Explanation

The normal distribution requires us to involve the z-score of watching TV for 10 hours a week.

The standardized score for any value is the value minus the mean then divided by the standard deviation.

z = (x - μ)/σ

x = 10 hours

μ = Mean = ?

σ = standard deviation = 2 hours

We are told that probability of watching the TV for more than 10 hours a week is 5%

P (x > 10) = 0.05

We can then put this in z-score form.

z-score of 10 hours = z

P (x > 10) = P (Z > z) = 0.05

So, to use the desmos calculator or the normal distribution table to first obtain z, we need to express the inequality in the form in which it exists in the tables or the calculator.

P (Z ≤ z)

= 1 - P (Z > z)

= 1 - 0.05

= 0.95

P (Z ≤ z) = 0.95

We can then use the calculator or the normal distribution to easily obtain z now.

To do that with the calculator, we just input the Cumulative probability and obtain the standardized score.

To do that with the normal distribution tables, we just look for the z-score that corresponds to 0.95

z = 1.645

z = (x - μ)/σ

x = 10 hours

μ = ?

σ = 2 hours

z = (x - μ)/σ

1.645 = (10 - μ)/2

10 - μ = (2) (1.645)

10 - μ = 3.29

μ = 10 - 3.29

μ = 6.71 hours

Hope this Helps!!!