james works an average of 22 hours per week with a standard deviation of 3.5 hours. what percentage of the time does james work more than 31 hours per week?
(31-22)/3.5 = 2.57
so look up Z>2.57 in your handy dandy Z table.
on davidmlane's page,
http://davidmlane.com/hyperstat/z_table.html
enter: mean = 22 , sd = 3.5
click on "above" and enter 31 to get
.0051
To find the percentage of the time James works more than 31 hours per week, we can use the concept of standard deviation and the normal distribution.
First, we need to calculate the z-score for the value of 31 hours. The z-score measures the number of standard deviations a value is away from the mean. It is calculated using the formula:
z = (x - μ) / σ
where:
x = value (31 hours in this case)
μ = mean (22 hours in this case)
σ = standard deviation (3.5 hours in this case)
Substituting the given values into the formula, we get:
z = (31 - 22) / 3.5
z = 9 / 3.5
z ≈ 2.57
Next, we can use a standard normal distribution table or a statistical calculator to find the percentage associated with a z-score of 2.57.
Looking up the z-score of 2.57 in a standard normal distribution table, we find that the percentage is approximately 99.49%. This represents the percentage of the time James works less than or equal to 31 hours per week.
To find the percentage of the time James works more than 31 hours per week, we subtract this percentage from 100%:
100% - 99.49% ≈ 0.51%
Therefore, James works more than 31 hours per week approximately 0.51% of the time.
Note: It's important to understand that this calculation assumes that James's working hours follow a normal distribution and that the data is accurate and representative.