Question

16. 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 8 bags contain fewer than 47 candies. How many bags were probably taken as samples?

Answer 1

I would say 16, because they have a standard deviation of 3 so their would be normally 47-53 candies in each bag so half are below and half are above 50

Answer 2

50 Bags

Explanation:

First, draw a normal distribution plot to use for the analysis of the data. Starting at the mean in the centre. Add one standard deviation for each interval to the right, and subtract one standard deviation for each interval to the right. See attached image. According to the empirical rule, 68% of data lies within one standard deviation of the mean, 95 % of the data is within two st. dev. and 99.7% of the data is within 3 st. dev. of the mean. Knowing this, it is concluded that 47 candies is one standard deviation from the mean.

That means that all the data to the left of that point is samples that contain less than 47 candies. Using the empirical method, the percentage to the right of the line can be calculated as 50 + 64/2 = 84%.

That means that 100 - 84 = 16% of the data is below 47.

`(8)/(samplesize) *100=16\\(8)/(samplesize) =0.16\\(8)/(0.16) =samplesize\\samplesize=50`