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# Case: DataStor Company

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Case Questions
1. Assuming that the DS4000 manufacturing process is functioning properly, what is the probability that DataStor falsely detects an early warning signal to a problem with quality using the tracking system that Escalera described? (Hint: DataStor will 'falsely detect' an early warning signal, if the process is functioning properly yet the tracking system will indicate a problem due to random chance.)

2. If the DS4000 hard drive process is functioning properly, what is the probability that a single shipment would be rejected by Four-D?

3. Still assuming that the process is functioning properly, what is the probability of four or more rejected shipments in 20 days?

4. Given the information in questions 1-3, and that Four-D did actually reject four of the last twenty shipments, is this evidence that the quality of the DS4000 has deteriorated, or do you believe that the rejected shipments are just due to random chance? Why or why not?

5. Use a graphical tool that describes the shape of the distribution of PDQ values. Verbally interpret the shape of the distribution. Do the data appear normally distributed?

6. Do the lower values of PDQ have anything in common? Are there any PDQ values below 6.2? Is this unusual?

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#### Solution Preview

See attached file for complete solution
1. Assuming that the DS4000 manufacturing process is functioning properly, what is the probability that DataStor falsely detects an early warning signal to a problem with quality using the tracking system that Escalera described? (Hint: DataStor will 'falsely detect' an early warning signal, if the process is functioning properly yet the tracking system will indicate a problem due to random chance.)

We asssume normal distribution

Mean=Mu = 6.8274 (Calculated above)
Standard deviation =s= 0.3233 (Calculated above)
PDQ= 6.2
z=(PDQ-Mu )/s= -1.9406 =(6.2-6.8274)/0.3233
Prob-value corresponding to z= -1.9406 is 2.615%

Answer: 2.615%

2. If the DS4000 hard drive process is functioning properly, what is the probability that a single shipment would be rejected by Four-D?

p= 2.615% ...

#### Solution Summary

Answers questions on case DataStor Company. (Adapted from Business Cases in Statistical Decision Making by L. H. Peters and J. B. Gray.) The question are on probability calculations using binomial and normal distribution.

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