If bolt thread length is normally distributed, what is the probability that the thread length of a randomly selected bolt is a.? ithin 1.5 SDs of its mean value? b.? ?Farther than 2.5 SDs from its mean value? c.? ?Between 1 and 2 SDs from its mean value?

Solution: Step 1: It is given that the bolt thread length is normally distributed, we have to find the probability that the thread length of normally selected bolt is Within 1.5SDs of its mean value Farther than 2.5SDs from its mean value. Between 1 and 2 SDs from its mean value. Step 2 : a) We have to find the probability that the length of a randomly selected bolt is within 1.5SDs of its mean value. Let X be the thread length of the bolt. It is given that the bolt thread length follow normal distribution. So it will be P(-1.5 z 1.5) = P( Z 1.5) - P(Z-1.5) From the standard normal table we will get the probability F(-1.5) = 0.9332 F( 1.5) = 0.0668 That is P(-1.5 z 1.5) = F( 1.5) - F(-1.5) = 0.8664 b) We have to find the probability that the thread length of randomly selected bolt is farther than 2.5 SDs from its mean value. That is The required probability = P(Z> 2.5) P(Z> 2.5) = 1-P(Z2.5) From the standard normal table we will get P(Z2.5) = 0.9938 P(Z> 2.5) = 1-0.9938 = 0.0062