Betty's Bite-Size Candies are packaged in bags. The number of candies per bag is normally distributed, with a mean of

Question

50 candies and a standard deviation of 3. At a quality control checkpoint, a sample of bags is checked, and 4 bags
contain fewer than 47 candies. How many bags were probably taken as samples?

(1 point)

25 bags

12 bags

8 bags

5 bags

Answer 1

8 bags

To calculate the number of bags that were probably taken as samples, we first need to determine the z-score for bags containing fewer than 47 candies.

z = (X - μ) / σ
Where X is the number of candies in each bag, μ is the mean (50 candies), and σ is the standard deviation (3 candies).

z = (47 - 50) / 3
z = -1

Using the z-table or a calculator, we can find that the probability of getting a z-score of -1 or less is approximately 0.1587. This represents the probability of getting a bag with fewer than 47 candies.

Since 4 bags were found to contain fewer than 47 candies, we can calculate the total probability of this happening in the sample of bags checked:

0.1587 x number of bags = 4
number of bags = 4 / 0.1587
number of bags ≈ 25.2

Therefore, approximately 25 bags were taken as samples.