select the correct answer from the drop - down menu.\nthe number of books borrowed from a library each week…

select the correct answer from the drop - down menu.\nthe number of books borrowed from a library each week follows a normal distribution. when a sample is taken for several weeks, the mean is found to be 190 and the standard deviation is 30.\nthere is a % chance that more than 250 books were borrowed in a week.

select the correct answer from the drop - down menu.\nthe number of books borrowed from a library each week follows a normal distribution. when a sample is taken for several weeks, the mean is found to be 190 and the standard deviation is 30.\nthere is a % chance that more than 250 books were borrowed in a week.

Answer

Answer:

(2.5)

Explanation:

Step1: Calculate the z - score

The formula for the z - score is (z=\frac{x-\mu}{\sigma}), where (x = 250), (\mu=190), and (\sigma = 30). [z=\frac{250 - 190}{30}=\frac{60}{30}=2]

Step2: Use the empirical rule

For a normal distribution:

  • Approximately (68%) of the data lies within (z=- 1) and (z = 1)
  • Approximately (95%) of the data lies within (z=-2) and (z = 2)
  • Approximately (99.7%) of the data lies within (z=-3) and (z = 3)

The percentage of data within (z=-2) and (z = 2) is (95%). So the percentage of data outside of (z=-2) and (z = 2) is (100%-95% = 5%). Since the normal distribution is symmetric, the percentage of data with (z>2) is (\frac{100% - 95%}{2}=2.5%)