Question

If bolt thread length is normally distributed, what is the probability that the thread length of a randomly selected bolt is (a) Within 1.3 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?

Answer 1

solution- Given. a) win in 13 SDs of its mean valuc? S P (lengin is within 1.3 50s of its mean value ) =P(2417) - - P(Z2-1.7) here we are supposed to normal distribution and normal value table. P= P(ZL17)- P(Z <= 17) = 0.95543 -0.04457 P: 0.91086 father than 2.1505 from its mean values P (length is within 2.150g of its mean values= P(Z22. 1)-P(21-21) P= P(Z <2.1) - P(24.2.1) 30.98214 - 0.0786 [p = 096488] P ( father than 2.150s from its mean value] =1-0.96428 p20.03572 c) between land 25os from its mean value: P(MAO EX L M+2) = 2P (14222) - 20.4772 -0.3413). 260.1359) 0.2718