The specifications of a particular component in a manufacturing process requires

Question

The specifications of a particular component in a manufacturing process requires that the length of the component be 25 mm. Due to the variation in the manufacturing process the components actually have a mean of 25 mm, a standard deviation of 2 mm and are normally distributed. 1. Specify the random variable of interest and its probability distribution. 2. If the length of the component is more than 30 mm, it will be discarded by the quality control check. What proportion of components discarded by quality control check? 3. What is the probability that the length of components will be between 22 and 28 mm?

Explanation / Answer

a)the random variable(X) in the length of the particularcomponen

it follows normal(25,2)

b)P(X>30)=P((X-25)/2>2.5)= 0.006209665

c)P(22<X<28)=P(22-25/5<X-25/2<28-25/3)= 0.8663856

Thanks

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