sorry to bother people with this, but my stats teacher did not make solving gaussian distribution questions, clear AT ALL in his notes, and my exam is coming soon, someone explain to me what is happening in here (like how the final answer is found)
P (X < 95.5) = P( (X − 98.8)/2 <( 95.5 − 98.8)/ 2) = P (Z < −1.65) = 0.0495
(heres the full question where the above was the solution)
- A machine is used to fill tubes, of nominal content 100 ml, with toothpaste. The amount of toothpaste delivered by the machine is normally distributed and may be set to any required mean value. Immediately after the machine has been over- hauled, the standard deviation of the amount delivered is 2 ml. As time passes, this standard deviation increases until the machine is again overhauled. The following three conditions are necessary for a batch of tubes of toothpaste to comply with current legislation: • I: the average content of the tubes must be at least 100 ml, • II: not more than 2.5% of the tubes may contain less than 95.5 ml, • III: not more than 0.1% of the tubes may contain less than 91 ml.
(a) For a batch of tubes with mean content 98.8 ml and standard deviation 2 ml,
find the proportion of tubes which contain i. less than 95.5 ml, Solution: Let X = amount of toothpaste in a tube (in ml). Then X ∼ G(98.8, 2).