Question

The contents (in g) of Fritz ketchup bottles are known to follow the Normal distribution with mean 452g and standard deviation 0.5g.

c) Find the percentage of bottles with contents that weigh between 452.5g and 453.5g.

i. Write a probability expression to find the answer: P( ____ )

ii. Complete the sketch of the density curve and shade the appropriate area.

iii. Find the probability.

d) What weight of ketchup content would approximately 16% of the bottles fall below?

i. Write a probability expression to find the answer: P( ____ )

ii. Complete the sketch of the density curve and shade the appropriate area.

iii. Find the weight.

Answer 1

Solution: It is given that:

c) Find the percentage of bottles with contents that weigh between 452.5g and 453.5g.

i. Write a probability expression to find the answer: P( ____ )

Answer:

ii. Complete the sketch of the density curve and shade the appropriate area.

Answer:

iii. Find the probability.

Using the z-score formula, we have:

  

Now using the standard normal table:

d) What weight of ketchup content would approximately 16% of the bottles fall below?

i. Write a probability expression to find the answer: P( ____ )

Answer:

ii. Complete the sketch of the density curve and shade the appropriate area.

Answer:

iii. Find the weight.

Answer: We have to first find the z-value corresponding to area = 0.16. Using the standard normal table, we have:

Now using the z-score formula, we have: