Question

A plastic bag manufacturer claims that the bags have a tear resistance (in Kg.) that is distributed N(10, 1):

a) We take 9 bags and get an average tear resistance of 9.5 Kg. ¿Should we believe the specifications provided by the manufacturer?

b) Find the probability that the bag will tear with 5 Kg. of oranges and 4 bottles of 1 liter of water whose containers weight 25 grs.

Answer 1

Let , X : Plastic bags tear resistance (in Kg)

a)

Hypothesis for the test is ,

Under , Test statistic is ,

Here , , , , .

Therefore ,

Therefore ,

Critical value / Table value :

For one tailed test &

Decision rule : If    then we reject at 5% level of significance .

Decision : Here ,

Therefore ,

.

Therefore , We cannot reject at 0.05 % level of significance .

Conclusion : We may conclude that we should believe the specifications provided by the manufacturer .

b)

As Bag containing 5 kg oranges And 4 bottles of 1 litre of water and container weight is 25 grams .

Since , one litre of water at 4 degree Celsius will exactly weigh equal to 1000 gram (1kg). At this temperature the density of water standard i. e. 1 gm/cubic centimeter. Or call it millilitre, the volume is the same.

4 litre of water have weight 4 kg .

Weight of container = 4* 25 = 100 grams = 0.1 kg

Total weight in the bag = weights of oranges + Weight of water + weight of container = 5 + 4 + 0.1 = 9.1 kg

Therefore ,probability that the bag will tear with 5 Kg. of oranges and 4 bottles of 1 liter of water whose containers weight 25 grs is given by ,

,

CONSIDER,

We know that

Therefore ,probability that the bag will tear with 5 Kg. of oranges and 4 bottles of 1 liter of water whose containers weight 25 grs is = = .

Probability that the bag will tear with 5 Kg. of oranges and 4 bottles of 1 liter of water whose containers weight 25 grs is 0.8159 .