what percentage of students studied between 30 and 40 hours? Range 10-50, Mean- 35, standard deviation-5.
Z = (score-mean)/SD
Find table in the back of your statistics text labeled something like "areas under normal distribution" to find the proportions related to the two Z scores.
It should be close to 68%.
To find the percentage of students who studied between 30 and 40 hours, we will use the Z-score formula. The Z-score measures the number of standard deviations an individual data point is from the mean.
The Z-score formula is:
Z = (X - μ) / σ
Where:
Z is the Z-score
X is the data point
μ is the mean
σ is the standard deviation
In our case, X1 = 30, X2 = 40, μ = 35, and σ = 5.
First, let's calculate the Z-score for X1 = 30:
Z1 = (30 - 35) / 5
Z1 = -1
Next, let's calculate the Z-score for X2 = 40:
Z2 = (40 - 35) / 5
Z2 = 1
Now, we can use the Z-score table or a calculator to find the area under the normal distribution curve between -1 and 1. This area represents the percentage of students who studied between 30 and 40 hours.
From the Z-score table, the area between -1 and 1 is approximately 0.6827. This means that approximately 68.27% of the students studied between 30 and 40 hours.
So, the percentage of students who studied between 30 and 40 hours is approximately 68.27%.