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Sagot :
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!!!
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