We can use the normal distribution to find the probability of getting 12 bags with fewer than 47 candies out of a sample of bags. First, we need to calculate the z-score for 47 candies:
z = (47 - 50) / 3 = -1
Now we use a standard normal distribution table or calculator to find the probability of getting a z-score of -1 or less, which is 0.1587. This means that there is a 15.87% chance of getting a bag with fewer than 47 candies in a random sample.
To find the number of bags that were probably taken as samples, we can use the formula:
n = (z * σ / E)^2
where n is the sample size, z is the z-score for the desired level of confidence (we'll assume z = 1.96 for a 95% confidence level), σ is the standard deviation, and E is the maximum error we are willing to tolerate (we'll assume E = 0.05).
Substituting the values, we get:
n = (1.96 * 3 / 0.05)^2 = 2662.56
Rounding up to the nearest whole number, we get:
n = 2663
Therefore, we can estimate that around 2663 bags were probably taken as samples to get 12 bags with fewer than 47 candies.
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 12 bags contain fewer than 47 candies. How many bags were probably taken as samples?
1 answer