The results of a survey showed that on average, children spend 5.6 hours at PlayStation per week. Suppose that the standard deviation is 1.7 hoursWhat is the z-value for a child who spends 7.5 hours at PlayStation per week?
Question
The results of a survey showed that on average, children spend 5.6 hours at PlayStation per week. Suppose that the standard deviation is 1.7 hoursWhat is the z-value for a child who spends 7.5 hours at PlayStation per week?
Solution
To calculate the z-value, you need to use the formula:
Z = (X - μ) / σ
where: X = value from the dataset (in this case, 7.5 hours) μ = mean of the dataset (in this case, 5.6 hours) σ = standard deviation of the dataset (in this case, 1.7 hours)
Substituting the values into the formula, we get:
Z = (7.5 - 5.6) / 1.7
Calculate the difference between X and μ:
7.5 - 5.6 = 1.9
Then divide the result by the standard deviation:
1.9 / 1.7 = 1.11764705882
So, the z-value for a child who spends 7.5 hours at PlayStation per week is approximately 1.12. This means that this child spends about 1.12 standard deviations more time on the PlayStation than the average child.
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