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Drums labeled 30 L are filled with a solution from a large

ISBN: 9780073401331 38

Solution for problem 8E Chapter 4.11

Statistics for Engineers and Scientists | 4th Edition

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Problem 8E

Drums labeled 30 L are filled with a solution from a large vat. The amount of solution put into each drum is random with mean 30.01 L and standard deviation 0.1 L.

a. What is the probability that the total amount of solution contained in 50 drums is more than 1500 L?

b. If the total amount of solution in the vat is 2401 L, what is the probability that 80 drums can be filled without running out?

c. How much solution should the vat contain so that the probability is 0.9 that 80 drums can be filled without running out?

Step-by-Step Solution:

Step 1 of 3:

(a)

In this question, we are asked to find the probability that the total amount of solution contained in 50 drums is more than 1500.

Drums labeled  are filled with a solution from a large vat.

The amount of solution has mean  and standard deviation .

We need to find

Let is the amount of solution in drums.

Let  = .

Hence  can be approximately normal distributed.

CLT specifies that and  for sum of the sample items.

Hence we achieve,

Mean

Standard deviation

Now we will calculate the  score because our distribution is approximately normal.

thus the  score of 1500  is

=

=

= -0.7071

From the z table, the area to the left of  is 0.2206.

Therefore

Hence the probability that the  total amount of solution contained in 50 drums is more than 1500is 0.7794.

Step 2 of 3:

(b)

In this question, we are asked to find the probability that 80 drums can be filled without running out.

If the total amount of solution in the vat is 2401.

We need to find

Let is the amount of solution in drums.

Let  = .

Mean

Standard deviation

.Now we will calculate the  score because our distribution is approximately normal.

thus the  score of 2401  is

=

=

= 0.2236

From the z table, the area to the left of  is 0.5948.

Therefore

Hence the probability that the  total amount of solution contained in 80 drums is 2401is 0.5948.

Step 3 of 3

ISBN: 9780073401331

This textbook survival guide was created for the textbook: Statistics for Engineers and Scientists , edition: 4. Since the solution to 8E from 4.11 chapter was answered, more than 1262 students have viewed the full step-by-step answer. The full step-by-step solution to problem: 8E from chapter: 4.11 was answered by , our top Statistics solution expert on 06/28/17, 11:15AM. Statistics for Engineers and Scientists was written by and is associated to the ISBN: 9780073401331. The answer to “Drums labeled 30 L are filled with a solution from a large vat. The amount of solution put into each drum is random with mean 30.01 L and standard deviation 0.1 L.a. What is the probability that the total amount of solution contained in 50 drums is more than 1500 L?________________b. If the total amount of solution in the vat is 2401 L, what is the probability that 80 drums can be filled without running out?________________c. How much solution should the vat contain so that the probability is 0.9 that 80 drums can be filled without running out?” is broken down into a number of easy to follow steps, and 98 words. This full solution covers the following key subjects: solution, drums, Probability, amount, filled. This expansive textbook survival guide covers 153 chapters, and 2440 solutions.

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