Question

The weights of pennies minted after 1982 are Normally distributed with mean 2.46 grams and standard deviation .02 grams.

1. For a penny to be among the heaviest 10% of all pennies, what must it weigh? (A sketch is often helpful for this type of problem)

2. Supposeasampleof10penniesisrandomlyselectedfromthepopulationof pennies. What is the probability that the average of this sample is more than 2.47 grams?

3. Now, instead, if a sample of 30 pennies is randomly selected from the population, what is the probability that the average of this sample is more than 2.47 grams?

4. Compare the probabilities in parts d. and e. Which is bigger? Briefly explain why this makes sense. You may answer this question with a picture if you’d like.

Answer 1