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Unit 15: Normal Probability Distribution

12. A firm buys springs in very large quantities and from past records it is known that 0.2% Notes
are defective. The inspection department sample the springs in batches of 500. It is required
to set a standard for the inspectors so that if more than the standard number of defectives
is found in a batch the consignment can be rejected with at least 90% confidence that the
supply is truly defective.
How many defectives per batch should be set as the standard?
13. Assume that your working hours X are distributed normally with m = 5 and s = 2. What is
the probability of your working 9 hours or more than 9 hours?
14. An assembly line contains 2,000 components each one of which has a limited life. Records
show that the life of the components is normally distributed with a mean of 900 hours and
a standard deviation of 80 hours.
(a) What proportion of components will fail before 1,000 hours?
(b) What proportion will fail before 750 hours?

(c) What proportion of components fail between 850 and 880 hours?
(d) Given that the standard deviation will remain at 80 hours what would the
average life have to be to ensure that not more than 10% of components fail before
900 hours?

Answers: Self Assessment

1. False 2. True
3. True 4. True

5. True 6. True
7. True 8. True
9. False 10. True
11. True 12. True
13. False 14. False

15. neither, nor 16. – , +
17. (b) 18. (c)

19. (a) 20. (c)
15.10 Further Readings

Books Balwani Nitin Quantitative Techniques, First Edition: 2002. Excel Books, New Delhi.
Bhardwaj R S., Business Statistics, Excel Books.
Garrett H.E (1956), Elementary Statistics, Longmans, Green & Co., New York.
Selvaraj R, Loganathan, C Quantitative Methods in Management.

Stockton and Clark, Introduction to Business and Economic Statistics, D.B. Taraporevala
Sons and Co. Private Limited, Bombay.

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