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You are a Business Analyst working for the ABC Ball Bearing company. An hour ago, you sent an order of 74 boxes of your A1 ball bearings to a customer on your delivery truck. You have just found out that your truck is going to go over a bridge that has a weight limit of 11,500 lbs. You need to determine if your truck will safely make it over the bridge. If you determine that the truck cannot make it over the bridge, you will need to call the driver and have him/her turn back.
The plant manager has told you that an empty delivery truck with the driver weighs about 8500 lbs.

You have 30 boxes of the A1 ball bearings in your plant. You immediately had them weighed. The weights of the boxes are:

40.1 41.1 39.5 40.1 39.1
41.2 37.6 39.1 41.6 40.8
43.2 38.9 38.1 43.5 36.9
39.1 40.5 41.2 37.6 44.0
38.0 39.8 42.1 38.6 41.3
43.7 36.9 43.6 38.1 40.2

1. Calculate the Mean and the Standard Deviation of this sample.

2. Using the normal distribution curve, calculate the probability the truck's total weight is under 11,500 lbs. What is your decision? Will you allow the truck to continue or will you call the driver and tell him/her to turn back? Show all of your calculations.

3, Discuss several types of sample: e.g. convenience sample, random sampling, stratified sampling, systematic sampling or cluster sampling. Discuss which type of sampling is used in this scenario.

4. Discuss what sampling bias is. Do you believer that using the 30 boxes in your warehouse cased sampling bias?

5. What does the central limit theorem state and why is it important to solving this problem. Is the thirty boxes of ball bearings enough to predict the probability of safely going over the bridge?

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Solution Summary

Step-by-step calculations and explanations are given. Calculator results are shown.

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1.
To calculate the mean, add the weights of the 30 boxes and divide the total by 30. A good calculator can be used to find the mean and standard deviation quickly. The following calculator was used:
https://www.calculator.net/standard-deviation-calculator.html

The results are shown

From the calculator, the mean is 40.18 and the standard deviation is 2.08.

2.
Each step of the calculation is shown below.

Step 1) The weight limit of the bridge is 11,500 lbs. The weight of the empty truck with the driver is 8,500 lbs.
11,500 - 8,500 = 3,000
Therefore, the total weight of the 74 boxes on the delivery truck cannot exceed 3,000 lbs.

Step 2) Find the average weight that each of the 74 boxes can be to safely cross the bridge.
3,000 / 74 = 40.54
To safely ...

Solution provided by:
J Pye, MSc
Education
  • MSc, California State Polytechnic University, Pomona
  • MBA, University of California, Riverside
  • BSc, California State Polytechnic University, Pomona
  • BSc, California State Polytechnic University, Pomona
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