9 4.E.044 If bolt thread length is norm ally distributed, what is the probabilit

Question

9 4.E.044 If bolt thread length is norm ally distributed, what is the probability that the thread length of a randomly selected bolt is (a) Within 1.4 SDs of its mean value? (b) Farther than 2.1 SDs from its mean value? (c) Between 1 and 2 SDs from its mean value? You may need to use the appropriate table in the Appendix of Tables to answer this question. Need Help?ReaTalik toa but can be reworked (rather than having to be scra Suppose that 1 of 200 shafts, and let X denote the number among these that are nonconforming and can be 888 a F1 esc

Explanation / Answer

a) P(Within 1.4 SDs of its mean value)

= P(-1.4 < z < 1.4)

= 0.8385

b) P(Farther than 2.1 SDs of its mean value)

= P(z < -2.1 or z > 2.1)

= 1 - P(-2.1 < z < 2.1)

= 1 - 0.9643

= 0.0357

c) P(Between 1 and 2 SDs)

= P(1 < z < 2)

= 0.1359

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