Question

Manufacturing companies strive to maintain production​ consistency, but it is often difficult for outsiders to tell whether they have succeeded. Consider a company that makes a certain brand of candy claims that 8​% the candies it produces are yellow and that bags are packed randomly. Their production controls can be checked by sampling bags of candies. Suppose bags containing about 300 candies are opened and the proportion of yellow candies is recorded. Complete parts a through c.

a) Explain why​ it's appropriate to use a Normal model to describe the distribution of the proportion of yellow candies they might expect in the 300​-candy bag. ​It's appropriate to use a Normal model because np=24 and nq=276​, which are both greater than or equal to 10. The samples in each bag should be random and independent.

Question: ​b) Use the 68−95−99.7 Rule to describe how this proportion might vary from bag to bag

Answer 1

Let denotes the sample proportion of yellow candies in a bag containing 300 candies.

or

Mean = 0.08

Standard deviation = 0.0156631

Using 68−95−99.7 rule, we can write

68% of proportions will lie between ( Mean - Standard deviation , Mean + Standard deviation) = (0.08 - 0.0156631, 0.08 + 0.0156631) =(0.0643369, 0.0956631)

95% of proportions will lie between ( Mean - 2*Standard deviation , Mean + 2*Standard deviation) = (0.08 - 2*0.0156631, 0.08 + 2*0.0156631) =(0.0486738, 0.1113262)

99.7% of proportions will lie between ( Mean - 2*Standard deviation , Mean + 2*Standard deviation) = (0.08 - 2*0.0156631, 0.08 + 2*0.0156631) =(0.0330107, 0.1269893)