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Bags checked for a certain airline flight have a mean

Statistics for Engineers and Scientists | 4th Edition | ISBN: 9780073401331 | Authors: William Navidi ISBN: 9780073401331 38

Solution for problem 5E Chapter 4.11

Statistics for Engineers and Scientists | 4th Edition

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Statistics for Engineers and Scientists | 4th Edition | ISBN: 9780073401331 | Authors: William Navidi

Statistics for Engineers and Scientists | 4th Edition

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Problem 5E

Bags checked for a certain airline flight have a mean weight of 15 kg with a standard deviation of 5 kg. A random sample of 60 bags is drawn.

a. What is the probability that the sample mean weight is less than 14 kg?

b. Find the 70th percentile of the sample mean weights.

c. How many bags must be sampled so that the probability is 0.01 that the sample mean weight is less than 14 kg?

Step-by-Step Solution:

Answer:

Step 1 of 3:

(a)

In this question, we are asked to find the probability that the sample mean weight is less than .

Mean weight of bag is  and standard deviation is kg.

A random sample of bags is drawn.

Let denote the drawn bags.

We need to find

Now the sample size is , which is a large sample.

Hence  can be approximately normal distributed.

CLT specifies that , variance  and standard deviation

Hence our sample mean and standard deviation is,

 

 = 0.6455

Therefore the  score of  14 is

=

=

 =

From the z table, the area to the left of   is 0.060.

Hence the probability that the sample mean weight is less than  is 0.060.


Step 2 of 3

Chapter 4.11, Problem 5E is Solved
Step 3 of 3

Textbook: Statistics for Engineers and Scientists
Edition: 4
Author: William Navidi
ISBN: 9780073401331

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Bags checked for a certain airline flight have a mean