Betty’s Bite-Size Candies are packaged in bags. The number of candies per bag is normally distributed, with a mean of 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?
To solve this problem, we can use the z-score formula:
z = (X - μ) / σ
Where:
- X is the observed value (in this case, 47 candies)
- μ is the mean number of candies per bag (50)
- σ is the standard deviation (3)
- z is the z-score
First, we calculate the z-score for 47 candies:
z = (47 - 50) / 3
z = -1
Next, we look up the z-score in a standard normal distribution table to find the probability of observing a value less than -1. The probability of observing a value less than -1 is approximately 0.1587.
Since 4 bags contain fewer than 47 candies, the probability of observing this outcome in a sample is 0.1587^4, or approximately 0.000413.
Therefore, the number of bags probably taken as samples is 1/0.000413, which is approximately 2419.