the times required to assemble a product part are normally distributed with a mean of 54.4 minutes & a standard deviation of 5.2 minutes. What fraction of the assemble workers require more than one hour?
Z = (score-mean)/SD
Convert hour into minutes.
Find table in the back of your statistics text labeled something like "areas under normal distribution" to find the proportion related to that Z score.
To find the fraction of assembly workers that require more than one hour to assemble a product part, we need to calculate the area under the normal curve beyond one hour (60 minutes).
First, we need to standardize the value of one hour using the Z-score formula:
Z = (X - μ) / σ
Where:
Z is the Z-score
X is the value we want to standardize (60 minutes in this case)
μ is the mean (54.4 minutes)
σ is the standard deviation (5.2 minutes)
Calculating the Z-score:
Z = (60 - 54.4) / 5.2
Z = 1.08
Next, we need to find the area under the normal curve beyond the Z-score of 1.08. We can use a standard normal distribution table or a calculator to find this area.
Using a standard normal distribution table, we find that the area to the right of Z = 1.08 is 0.1401 (approximately).
Therefore, the fraction of assembly workers that require more than one hour (60 minutes) is 0.1401 or approximately 14.01%.
Note: This means that about 14.01% of the assembly workers take longer than one hour to complete the assembly task.