Final answer:
A z-score calculation is used to find that there is a 2.28% chance that more than 250 books were borrowed from the library in a given week.
Step-by-step explanation:
The student’s question asks for the percentage chance that more than 250 books were borrowed in a week given that the number of books borrowed follows a normal distribution, where the sample mean is 190, and the sample standard deviation is 30.
To answer this, we’ll need to calculate the z-score for 250 books using the formula:
Z = (X - μ) / σ
Where X is 250 books, μ (mu) is the mean (190 books), and σ (sigma) is the standard deviation (30 books). Substituting these values, we get:
Z = (250 - 190) / 30 = 60 / 30 = 2
After calculating the z-score, we look up this value in the z-table to find the probability to the left of z=2. The table gives us the area under the curve to the left of the z-score. Since we’re interested in the probability of borrowing more than 250 books, we need to find the area to the right of z=2. This is equal to 1 minus the area to the left. Typically, the area to the left of z=2 is approximately 0.9772, which when subtracted from 1 gives us about 0.0228 or 2.28%.
Therefore, there is a 2.28% chance that in any given week, more than 250 books were borrowed.