Question

On the Elf’s contract, it states that he must deliver 5 pounds of candy to every house on the average.  However, his supervisor, Santa, feels that the Elf might be snacking along the way and not meeting this quota.  To monitor the Elf’s work, Santa took a random sample of 64 houses and the amount of candy delivered by the Elf was noted.  Assume: standard deviation of the amount of candy delivered to all the houses by the Elf is .6 pounds and the mean is 7 pounds.

a) What is the probability that the average amount of candy delivered to the 64 houses is more than 5.8 pounds?

b) Instead of 64 houses, Santa decided to sample 16 houses in order to save time.  What is the probability that the average amount of candy delivered to the 16 houses is less than 6 pounds?  What assumption/s do you need to answer this problem?  

Answer 1

a)

Let X denote the amount of candy delivered to the house (in pounds).

Using Central Limit theorem, we know,

Required probability =

b)

Assumption - We know that the Central limit thoerem holds for a large sample irrespective of the parent population.

Since this is a small sample case, so we need to assume that the parent population of amount of candy delivered to the house (in pounds) is Normal.

Using Central Limit theorem, we know,

Required probability =