Question

A marble factory produces marbles that weigh 10 grams apiece. The standard deviation of the weight of a bag of 100 marbles is 20 grams. You buy a bag of 100 marbles that weighs 960 grams.

You are 95% sure that the bag of marbles you purchased did not come from the factory.

True
False

Answer 1

If each marble is 10g, with 100 in the pack, the pack will weigh 1000g.
This is more than the 20g deviation, so the marbles did not come from this factory.
So the answer to your question is True

Answer 2

True

Explanation:

Given that A marble factory produces marbles that weigh 10 grams apiece.

The std deviation is 20 grams for a bag of 100 marbles.

Sample is the bag purchased

Sample weight = 960 grams

Population weight (given by factory) = 1000 gms.

Difference = sample weight -population weight = -40 gm

Std dev for 100 marbles = 20 gram

`Z = (-40)/(20)`=-2

Z critical value for 95% =1.96

Since our Z lies outside -1.96 and 1.96 we cannot be 95% sure that the bag of marbles you purchased did not come from the factory.